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Wyświetlanie 1-15 z 254
Tytuł:
Category theorems concerning Z-density continuous functions
Autorzy:
Ciesielski, K.
Larson, L.
Powiązania:
https://bibliotekanauki.pl/articles/1215085.pdf
Data publikacji:
1991
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
ℑ-density topology
ℑ-density continuous functions
first category sets
Opis:
The ℑ-density topology $T_ℑ$ on ℝ is a refinement of the natural topology. It is a category analogue of the density topology [9, 10]. This paper is concerned with ℑ-density continuous functions, i.e., the real functions that are continuous when the ℑ-density} topology is used on the domain and the range. It is shown that the family $C_ℑ$ of ordinary continuous functions f: [0,1]→ℝ which have at least one point of ℑ-density continuity is a first category subset of C([0,1])= {f: [0,1]→ℝ: f is continuous} equipped with the uniform norm. It is also proved that the class $C_ℑℑ$ of ℑ-density continuous functions, equipped with the topology of uniform convergence, is of first category in itself. These results remain true when the ℑ-density topology is replaced by the deep ℑ-density topology.
Źródło:
Fundamenta Mathematicae; 1991-1992, 140, 1; 79-85
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Vietoris system in strong shape and strong homology
Autorzy:
Günther, Bernd
Powiązania:
https://bibliotekanauki.pl/articles/1214990.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
vietoris nerve
Steenrod homotopy category
strong shape theory
strong homology
compact supports
Opis:
We show that the Vietoris system of a space is isomorphic to a strong expansion of that space in the Steenrod homotopy category, and from this we derive a simple description of strong homology. It is proved that in ZFC strong homology does not have compact supports, and that enforcing compact supports by taking limits leads to a homology functor that does not factor over the strong shape category. For compact Hausdorff spaces strong homology is proved to be isomorphic to Massey's homology.
Źródło:
Fundamenta Mathematicae; 1992, 141, 2; 147-168
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On open maps of Borel sets
Autorzy:
Ostrovsky, A.
Powiązania:
https://bibliotekanauki.pl/articles/1208391.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
open maps
Borel sets
analytic sets
space of the first category
space of the second category
Baire space
Opis:
We answer in the affirmative [Th. 3 or Corollary 1] the question of L. V. Keldysh [5, p. 648]: can every Borel set X lying in the space of irrational numbers ℙ not $G_δ · F_σ$ and of the second category in itself be mapped onto an arbitrary analytic set Y ⊂ ℙ of the second category in itself by an open map? Note that under a space of the second category in itself Keldysh understood a Baire space. The answer to the question as stated is negative if X is Baire but Y is not Baire.
Źródło:
Fundamenta Mathematicae; 1994-1995, 146, 3; 203-213
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Dugundji extension property can fail in ωµ -metrizable spaces
Autorzy:
Stares, Ian
Vaughan, Jerry
Powiązania:
https://bibliotekanauki.pl/articles/1205494.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Dugundji extension theorem
$ω_μ$-metrizable spaces
box topology
Baire category
Michael line
Opis:
We show that there exist $ω_μ$-metrizable spaces which do not have the Dugundji extension property ($2^{ω_1}$ with the countable box topology is such a space). This answers a question posed by the second author in 1972, and shows that certain results of van Douwen and Borges are false.
Źródło:
Fundamenta Mathematicae; 1996, 150, 1; 11-16
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Lie algebras in braided categories
Autorzy:
Pareigis, Bodo
Powiązania:
https://bibliotekanauki.pl/articles/1342720.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
braided category
universal enveloping algebra
braided Hopf algebra
graded Lie algebra
Opis:
The category of group-graded modules over an abelian group $G$ is a monoidal category. For any bicharacter of $G$ this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have $n$-ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are noncommutative noncocommutative Hopf algebras some of them known in the literature. Conversely the primitive elements of a Hopf algebra in the category form a Lie algebra in the above sense.
Źródło:
Banach Center Publications; 1997, 40, 1; 139-158
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fundamental pro-groupoids and covering projections
Autorzy:
Hernández-Paricio, Luis
Powiązania:
https://bibliotekanauki.pl/articles/1205368.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
covering projection
covering transformation
pro-groupoid, Čech fundamental pro-groupoid
covering reduced sieve
locally constant presheaf
category of fractions
subdivision
fundamental groupoid
Čech fundamental group
G-sets
continuous G-sets
Opis:
We introduce a new notion of covering projection E → X of a topological space X which reduces to the usual notion if X is locally connected. We use locally constant presheaves and covering reduced sieves to find a pro-groupoid π crs (X) and an induced category pro (π crs (X), Sets) such that for any topological space X the category of covering projections and transformations of X is equivalent to the category pro (π crs (X), Sets). We also prove that the latter category is equivalent to pro (π CX, Sets), where π CX is the Čech fundamental pro-groupoid of X. If X is locally path-connected and semilocally 1-connected, we show that π crs (X) is weakly equivalent to π X, the standard fundamental groupoid of X, and in this case pro (π crs (X), Sets) is equivalent to the functor category $Sets^{π X}$. If (X,*) is a pointed connected compact metrisable space and if (X,*) is 1-movable, then the category of covering projections of X is equivalent to the category of continuous $\check π_1 (X,*)$-sets, where $\check π_1 (X,*)$ is the Čech fundamental group provided with the inverse limit topology.
Źródło:
Fundamenta Mathematicae; 1998, 156, 1; 1-31
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category
Autorzy:
Bryden, J.
Zvengrowski, P.
Powiązania:
https://bibliotekanauki.pl/articles/1341772.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
cup products
cup product length
Lusternik-Schnirelmann category
degree one maps
diagonal map
Seifert manifolds
cohomology algebra
Opis:
This note gives a complete description of the cohomology algebra of any orientable Seifert manifold with ℤ/p coefficients, for an arbitrary prime p. As an application, the existence of a degree one map from an orientable Seifert manifold onto a lens space is completely determined. A second application shows that the Lusternik-Schnirelmann category for a large class of Seifert manifolds is equal to 3, which in turn is used to verify the Ganea conjecture for these Seifert manifolds.
Źródło:
Banach Center Publications; 1998, 45, 1; 25-39
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On exponentiation on n-ary hyperalgebras
Autorzy:
Bednařík, František
Šlapal, Josef
Powiązania:
https://bibliotekanauki.pl/articles/728790.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
n-ary hyperalgebra
medial hyperalgebra
diagonalhyperalgebra
power of hyperalgebras
cartesian closed category
Opis:
For n-ary hyperalgebras we study a binary operation of exponentiation which to a given pair of n-ary hyperalgebras assigns their power, i.e., an n-ary hyperalgebra carried by the corresponding set of homomorphisms. We give sufficient conditions for the existence of such a power and for a decent behaviour of the exponentiation. As a consequence of our investigations we discover a cartesian closed subcategory of the category of n-ary hyperalgebras and homomorphisms between them.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 1; 13-19
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the structure of halfdiagonal-halfterminal-symmetric categories with diagonal inversions
Autorzy:
Vogel, Hans-Jürgen
Powiązania:
https://bibliotekanauki.pl/articles/728750.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
halfdiagonal-halfterminal-symmetric category
diagonal inversion
partial order relation
subidentity
equation
Opis:
The category of all binary relations between arbitrary sets turns out to be a certain symmetric monoidal category Rel with an additional structure characterized by a family $d = (d_{A}: A → A⨂ A | A ∈ |Rel|)$ of diagonal morphisms, a family $t = (t_{A}: A → I | A ∈ |Rel|)$ of terminal morphisms, and a family $∇ = (∇_{A}: A ⨂ A → A | A ∈ |Rel|)$ of diagonal inversions having certain properties. Using this properties in [11] was given a system of axioms which characterizes the abstract concept of a halfdiagonal-halfterminal-symmetric monoidal category with diagonal inversions (hdht∇s-category). Besides of certain identities this system of axioms contains two identical implications. In this paper is shown that there is an equivalent characterizing system of axioms for hdht∇s-categories consisting of identities only. Therefore, the class of all small hdht∇-symmetric categories (interpreted as hetrogeneous algebras of a certain type) forms a variety and hence there are free theories for relational structures.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 2; 139-163
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kategoria genezy w protobiologii − aspekt bioelektroniczny
The Category of Genesis in Protobiology − Bioelectronic Aspect
Autorzy:
Wnuk, Marian
Powiązania:
https://bibliotekanauki.pl/articles/2015872.pdf
Data publikacji:
2002
Wydawca:
Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
Tematy:
powstanie życia
protobiologia
bioelektronika
kategoria genezy
biosystemogeneza
sprzężenie chemiczno-elektroniczne
elektromagnetyczna natura życia
biosystemy
abiogeneza
origin of life
protobiology
bioelectronics
category of genesis
biosystemogenesis
chemical-electronic coupling
electromagnetic nature of life
biosystems
abiogenesis
Opis:
Protobiology as a science about the origin of life is based on the idea of chemical evolution. The bioelectronics conception, however, that life is a form of electromagnetic information suggests that it is not „chemical evolution” but „evolution of information” that can be accepted as a more basic one. The paper sought to develop, within the context of biosystemogenesis, the idea of a chemical-electronic coupling in organisms (the so-called quantum seam of life). The „quantum seam of life” is a thermodynamically optimal and open quantum system in which chemical and electronic process come about. It exists owing to electromagnetic information and manifests self-synchronization, metastable energetic state, and constant properties independent of evolution. From the point of view of the electromagnetic conception of the nature of life, the category of genesis (i.e. the genesis of life or biosystems) may be understood in a broader manner than it has been done up to now. First of all, it can be understood as electromagnetic biosystemogenesis. The life of earth would originate in information whose bearer was the electromagnetic field. Philosophical implications of this statement are discussed in the paper. It is suggested that nanotechnology and quantum optoelectronics may provide new possibilities of how to empirically test electromagnetic biosystemogenesis and the idea of the evolution of information. The significance of the concept of genesis may be of key importance for the models suggesting new, more adequate scenarios of the processes of the origin of life.
Źródło:
Roczniki Filozoficzne; 2002, 50, 3; 199-203
0035-7685
Pojawia się w:
Roczniki Filozoficzne
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Metaphysical Principles of Genesis
Metafizyczne zasady genezy
Autorzy:
Stanciene, Dalia Marija
Powiązania:
https://bibliotekanauki.pl/articles/2015905.pdf
Data publikacji:
2002
Wydawca:
Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
Tematy:
kategoria genezy
metafizyka
Arystoteles
filozofia
natura
category of genesis
metaphysics
Aristotle
philosophy
nature
Opis:
Analiza historii filozofii i nauki starożytnej Grecji pokazuje, iż problemem matematycznym było stworzenie nauki przyrodniczej. Wszelkie wysiłki w celu uczynienia z matematyki, w której centrum znajdujemy statyczne formy geometryczne, nauki wyjaśniającej zasady ruchu, zmiany, stawania się i zanikania rzeczy nie przyniosły spodziewanych rezultatów. Badacze doszli do wniosku, że widzialny świat jest raczej przedmiotem różnych poglądów, ale nie nauki (zob. np. Platon, Timajos, 29). Niemniej jednak myśl, że matematyka jest istotna dla nauk przyrodniczych, była słuszna. Księga przyrody została napisana językiem matematyki − takie jest motto fizyki New Age. Trzeba by teraz pokazać konkretnie, jak język matematyki potrafi opisać zmiany. Matematyka starożytnej Grecji nie była gotowa do wypełnienia tego zadania. Grecy mieli do wyboru albo zrezygnować z projektu tworzenia nauki przyrody, albo zbudować ją na czymś innym. Arystoteles wybrał tę drugą możliwość. Oparł fizykę na metafizyce zamiast na matematyce i stworzył pierwszą naukową teorię przyrody, która obowiązywała przez stulecia, dopóki nie została zastąpiona (i to niezupełnie w sposób pokojowy) przez bardziej naukową fizykę matematyczną. Newtona ostrzeżenie brzmi: fizyka odrzuca metafizykę, odzwierciedla kolizję pomiędzy fizyką Arystotelesowską i fizyką New Age. Powstaje pytanie, czy fizyka Arystotelesa stymulowała, czy też hamowała rozwój nauk przyrodniczych. Odpowiedź na tę kwestię winna zainteresować myślicieli katolickich ze względu na bezpośrednie powiązanie z tomizmem.
An analysis of the history of philosophy and science in ancient Greece shows that the mathematical problem was to create natural science. All efforts to make mathematics at the center of which we find static geometric form, a science explaining the principles of things moving, changing, becoming, and disappearing have failed to produce the expected results. The researchers concluded that the visible world is the subject of different views rather than science (see, e.g., Plato, Timajos, 29). Nevertheless, it was correct to think that mathematics was essential to the natural sciences. The Book of Nature was written in the language of mathematics, and this is the motto of New Age physics. Now it would be necessary to show specifically how the language of mathematics can describe changes. Ancient Greek mathematics was not ready for this task. The Greeks had the choice of either giving up the project of creating a natural science or building it on something else. Aristotle chose the latter. He based physics on metaphysics instead of mathematics and created the first scientific theory of nature that was valid for centuries until it was replaced (and not entirely peacefully) by more scientific mathematical physics. Newton warns: physics rejects metaphysics; it reflects the collision between Aristotle's physics and New Age physics. The question arises whether Aristotle's physics stimulated or hindered the development of natural sciences. The answer to this question should be of interest to Catholic thinkers because of its direct connection with Thomism.
Źródło:
Roczniki Filozoficzne; 2002, 50, 3; 41-46
0035-7685
Pojawia się w:
Roczniki Filozoficzne
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On generalized Hom-functors of certain symmetric monoidal categories
Autorzy:
Vogel, Hans
Powiązania:
https://bibliotekanauki.pl/articles/729029.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
symmetric monoidal category
monoidal functor
Hom-functor
Opis:
It is well-known that for each object A of any category C there is the covariant functor $H^{A}: C → Set$, where $H^{A}(X)$ is the set C[A,X] of all morphisms out of A into X in C for an arbitrary object X ∈ |C| and $H^{A}(φ)$, φ ∈ C[X,Y], is the total function from C[A,X] into C[A,Y] defined by C[A,X] ∋ u → uφ ∈ C[A,Y].
If C̲ is a dts-category, then $H^{A}$ is in a natural manner a d-monoidal functor with respect to
$\tilde{H^{A}} = $\tilde{H^{A}}⟨X,Y⟩: C[A,X] × C[A,Y] → C[A,X⊗Y]$,
$((u₁,u₂) ↦ d_{A}(u₁⊗u₂)) | X,Y ∈ |C|)$
and
$i_{H^{A}}:{∅} → C[A,I], (∅ ↦ t_{A})$.
This construction can be generalized to functors $H^{e}$ from any dhth∇s-category K̲ into the category P̲a̲r̲ related to arbitrary subidentities e of K̲ (cf. S [3]). Each such generalized Hom-functor $H^{e}$ related to any subidentity $e ≤ 1_{A}$, $o_{A,A} ≠ e$, turns out to be a monoidal dhth∇s-functor from K̲ into P̲a̲r̲.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2002, 22, 1; 47-71
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adjointness between theories and strict theories
Autorzy:
Vogel, Hans-Jürgen
Powiązania:
https://bibliotekanauki.pl/articles/728926.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
symmetric monoidal category
dhts-category
partial theory
adjoint functor
Opis:
The categorical concept of a theory for algebras of a given type was foundet by Lawvere in 1963 (see [8]). Hoehnke extended this concept to partial heterogenous algebras in 1976 (see [5]). A partial theory is a dhts-category such that the object class forms a free algebra of type (2,0,0) freely generated by a nonempty set J in the variety determined by the identities ox ≈ o and xo ≈ o, where o and i are the elements selected by the 0-ary operation symbols.
If the object class of a dhts-category forms even a monoid with unit element I and zero element O, then one has a strict partial theory.
In this paper is shown that every J-sorted partial theory corresponds in a natural manner to a J-sorted strict partial theory via a strongly d-monoidal functor. Moreover, there is a pair of adjoint functors between the category of all J-sorted theories and the category of all corresponding J-sorted strict theories.
This investigation needs an axiomatic characterization of the fundamental properties of the category Par of all partial function between arbitrary sets and this characterization leads to the concept of dhts- and dhth∇s-categories, respectively (see [5], [11], [13]).
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2003, 23, 2; 163-212
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
06 условности грамматического лица в художественном повествовании
Autorzy:
Axmetoba, Гaлия Д.
Powiązania:
https://bibliotekanauki.pl/articles/1925990.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Opolski
Tematy:
the relative statuse of the grammatical category of person
method of composition
fictional narration
linguislic composition
image of the author
word variety
compositional-stylistic aspect
Opis:
According to the analysis of the text of the contemporary fiction this article performs the clescription of the new phenomena (equally with the development of the traditions ofthe realistic fiction) concerring the reflection of the narrator's person. It is typical of a fictional narration to con ta in various chan ges of different grammatical categories of person(«aplay with persons» ). The contemporary fiction ten ds to realize a special method of composition when the grammatical category of person has a relative statuse.
Źródło:
Stylistyka; 2005, 14; 587-600
1230-2287
2545-1669
Pojawia się w:
Stylistyka
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Categories of functors between categories with partial morphisms
Autorzy:
Vogel, Hans-Jürgen
Powiązania:
https://bibliotekanauki.pl/articles/729097.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
symmetric monoidal category
dhts-category
Hoehnke category
Hoehnke theory
monoidal functor
d-monoidal functor
dht-symmetric functor
functor composition
cartesian product
Opis:
It is well-known that the composition of two functors between categories yields a functor again, whenever it exists. The same is true for functors which preserve in a certain sense the structure of symmetric monoidal categories. Considering small symmetric monoidal categories with an additional structure as objects and the structure preserving functors between them as morphisms one obtains different kinds of functor categories, which are even dt-symmetric categories.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2005, 25, 1; 39-87
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
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