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Wyświetlanie 1-15 z 157
Tytuł:
Fuzzy mappings
Autorzy:
Heilpern, Stanisław
Powiązania:
https://bibliotekanauki.pl/articles/747379.pdf
Data publikacji:
1983
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Fuzzy topology
Fuzzy set theory
Fixed-point and coincidence theorems
Opis:
.
Let X be the class of all fuzzy subsets of a metric space X. A fuzzy subset A is called an approximate value if A is a closed and convex fuzzy subset with supA(x)=1; the class of all such elements is denoted by W(X), and it is a metric space with the distance D(A,B)=sup dist(Aα,Bα), where Aα and Bα denote the α-level of A and B, respectively, and dist( , ) denotes the generalized Hausdorff distance [see, e.g., M. P. Chen and M. H. Shin , J. Math. Anal. Appl. 71 (1979), no. 2, 516–524; MR0548780]. The author is especially concerned with W(R). Algebraic operations in W(R) are defined and basic rules for arithmetic operations on approximate values are proved. Moreover, functions with values in W(R) are also investigated. Finally, a fixed point theorem for fuzzy mappings is stated and an example is given [for the proof see the author, ibid. 83 (1981), no. 2, 566–569; MR0641351].
Źródło:
Mathematica Applicanda; 1983, 11, 22
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
A contribution to the topological classification of the spaces Ср(X)
Autorzy:
Cauty, Robert
Dobrowolski, Tadeusz
Marciszewski, Witold
Powiązania:
https://bibliotekanauki.pl/articles/1208632.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
function space
pointwise convergence topology
absorbing sets
Borel and projective filters
Opis:
We prove that for each countably infinite, regular space X such that $C_p(X)$ is a $Z_σ$-space, the topology of $C_p(X)$ is determined by the class $F_0(C_p(X))$ of spaces embeddable onto closed subsets of $C_p(X)$. We show that $C_p(X)$, whenever Borel, is of an exact multiplicative class; it is homeomorphic to the absorbing set $Ω_α$ for the multiplicative Borel class $M_α$ if $F_0(C_p(X)) = M_α$. For each ordinal α ≥ 2, we provide an example $X_α$ such that $C_p(X_α)$ is homeomorphic to $Ω_α$.
Źródło:
Fundamenta Mathematicae; 1993, 142, 3; 269-301
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hyperspaces of CW-complexes
Autorzy:
Guo, Bao-Lin
Sakai, Katsuro
Powiązania:
https://bibliotekanauki.pl/articles/1208620.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
CW-complex
hyperspace
the Vietoris topology
stratifiable space
AR(S)
ANR(S)
Opis:
It is shown that the hyperspace of a connected CW-complex is an absolute retract for stratifiable spaces, where the hyperspace is the space of non-empty compact (connected) sets with the Vietoris topology.
Źródło:
Fundamenta Mathematicae; 1993, 143, 1; 23-40
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Intersection topologies with respect to separable GO-spaces and the countable ordinals
Autorzy:
Jones, M.
Powiązania:
https://bibliotekanauki.pl/articles/1208416.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
intersection topology
GO-space
separable
subtopology
normality
$ω_1$-compactness
countable ordinals
Opis:
Given two topologies, $T_1$ and $T_2$, on the same set X, the intersection topology} with respect to $T_1$ and $T_2$ is the topology with basis ${U_1 ∩ U_2 :U_1 ∈ T_1, U_2 ∈ T_2}$. Equivalently, T is the join of $T_1$ and $T_2$ in the lattice of topologies on the set X. Following the work of Reed concerning intersection topologies with respect to the real line and the countable ordinals, Kunen made an extensive investigation of normality, perfectness and $ω_1$-compactness in this class of topologies. We demonstrate that the majority of his results generalise to the intersection topology with respect to an arbitrary separable GO-space and $ω_1$, employing a well-behaved second countable subtopology of the separable GO-space.
Źródło:
Fundamenta Mathematicae; 1994-1995, 146, 2; 153-158
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The hyperspace of finite subsets of a stratifiable space
Autorzy:
Cauty, Robert
Guo, Bao-Lin
Sakai, Katsuro
Powiązania:
https://bibliotekanauki.pl/articles/1208364.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
hyperspace
the Vietoris topology
stratifiable space
AR(S), ANR(S)
2-hyper-locally-connected
Opis:
It is shown that the hyperspace of non-empty finite subsets of a space X is an ANR (an AR) for stratifiable spaces if and only if X is a 2-hyper-locally-connected (and connected) stratifiable space.
Źródło:
Fundamenta Mathematicae; 1995, 147, 1; 1-9
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Ramsey, Lebesgue, and Marczewski sets and the Baire property
Autorzy:
Reardon, Patrick
Powiązania:
https://bibliotekanauki.pl/articles/1205503.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Ramsey set
Marczewski set
perfect set
measurable set
Baire property
density topology
Ellentuck topology
σ-algebra
Opis:
We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented.

 THEOREM. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets.

 THEOREM. In the Ellentuck topology on $[ω]^ω$, $(s)_0$ is a proper subset of the hereditary ideal associated with (s).

 We construct an example in the Ellentuck topology of a set which is first category and measure 0 but which is not $B_r$-measurable. In addition, several theorems concerning perfect sets in the Ellentuck topology are presented. In particular, it is shown that there exist countable perfect sets in the Ellentuck topology.
Źródło:
Fundamenta Mathematicae; 1996, 149, 3; 191-203
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Selections that characterize topological completeness
Autorzy:
van Mill, Jan
Pelant, Jan
Pol, Roman
Powiązania:
https://bibliotekanauki.pl/articles/1205513.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
selection
Vietoris topology
completely metrizable
Opis:
We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].
Źródło:
Fundamenta Mathematicae; 1996, 149, 2; 127-141
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:
A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ
Autorzy:
Marciszewski, Witold
Powiązania:
https://bibliotekanauki.pl/articles/1205429.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
function space
pointwise convergence topology
$c_p(X)$
linear homeomorphism
Opis:
We construct two examples of infinite spaces X such that there is no continuous linear surjection from the space of continuous functions $c_p(X)$ onto $c_p(X)$ × ℝ$. In particular, $c_p(X)$ is not linearly homeomorphic to $c_p(X)$ × ℝ$. One of these examples is compact. This answers some questions of Arkhangel'skiĭ.
Źródło:
Fundamenta Mathematicae; 1997, 153, 2; 125-40
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The sequential topology on complete Boolean algebras
Autorzy:
Główczyński, Wiesław
Balcar, Bohuslav
Jech, Thomas
Powiązania:
https://bibliotekanauki.pl/articles/1205404.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
complete Boolean algebra
sequential topology
Maharam submeasure
sequential cardinal
Opis:
We investigate the sequential topology $τ_{s}$ on a complete Boolean algebra B determined by algebraically convergent sequences in B. We show the role of weak distributivity of B in separation axioms for the sequential topology. The main result is that a necessary and sufficient condition for B to carry a strictly positive Maharam submeasure is that B is ccc and that the space $(B,τ_{s})$ is Hausdorff. We also characterize sequential cardinals.
Źródło:
Fundamenta Mathematicae; 1998, 155, 1; 59-78
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Mackey topology for groups
Autorzy:
Chasco, M.
Martín-Peinador, E.
Tarieladze, V.
Powiązania:
https://bibliotekanauki.pl/articles/1217305.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
locally convex space
Mackey topology
continuous character
weakly compact
locally quasi-convex group
Opis:
The present paper is a contribution to fill in a gap existing between the theory of topological vector spaces and that of topological abelian groups. Topological vector spaces have been extensively studied as part of Functional Analysis. It is natural to expect that some important and elegant theorems about topological vector spaces may have analogous versions for abelian topological groups. The main obstruction to get such versions is probably the lack of the notion of convexity in the framework of groups. However, the introduction of quasi-convex sets and locally quasi-convex groups by Vilenkin [26] and the work of Banaszczyk [1] have paved the way to obtain theorems of this nature. We study here the group topologies compatible with a given duality. We have obtained, among others, the following result: for a complete metrizable topological abelian group, there always exists a finest locally quasi-convex topology with the same set of continuous characters as the original topology. We also give a description of this topology as an S-topology and we prove that, for the additive group of a complete metrizable topological vector space, it coincides with the ordinary Mackey topology.
Źródło:
Studia Mathematica; 1999, 132, 3; 257-284
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the evaluation of compatibility with gradual rules in information systems : a topological approach
Autorzy:
Kortelainen, J.
Powiązania:
https://bibliotekanauki.pl/articles/205981.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
analiza danych
topologia
zbiór rozmyty
data analysis
knowledge acquisition
L-fuzzy sets
modifier logic
rough sets
topology
Opis:
The paper presents an approach to detecting dependence of a decision-maker's actions (or decisions) on conditions with respect to a certain type of fuzzy rules, namely gradual rules. Gradual rules are of the form "the more c is C, the more d is D", where C and D are L-fuzzy sets on the domain of the attributes c and d with membership values possibly in different lattices, respectively. The decision-maker's actions and conditions for those are found in a data base-like system, called an information system. We use the information system to define relations corresponding to L-fuzzy sets, and we define weakening modifiers by these relations. These modifiers are closure operators in the corresponding topologies, and we can define fineness relation between L-fuzzy sets. This relation is useful when comparing different decision-maker's actions. We define strong degree and topological degree of depedence of the attributes (with respect to a gradual rule), and we study some properties of those. Finally, we present a small application.
Źródło:
Control and Cybernetics; 1999, 28, 1; 121-131
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The concept of boundedness and the Bohr compactification of a MAP Abelian group
Autorzy:
Galindo, Jorge
Hernández, Salvador
Powiązania:
https://bibliotekanauki.pl/articles/1205259.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Bohr topology
LCA group
$ℒ_∞$-group
boundedness
locally convex vector space
DF-space
maximally almost periodic
respects compactness
C-embedded
C*-embedded
Opis:
Let G be a maximally almost periodic (MAP) Abelian group and let ℬ be a boundedness on G in the sense of Vilenkin. We study the relations between ℬ and the Bohr topology of G for some well known groups with boundedness (G,ℬ). As an application, we prove that the Bohr topology of a topological group which is topologically isomorphic to the direct product of a locally convex space and an $ℒ_∞$-group, contains "many" discrete C-embedded subsets which are C*-embedded in their Bohr compactification. This result generalizes an analogous theorem of van Douwen for the discrete case and some other ones due to Hartman and Ryll-Nardzewski concerning the existence of $I_0$-sets. We also obtain some results on preservation of compactness for the Bohr topology of several types of MAP Abelian groups, like $ℒ_∞$-groups, locally convex vector spaces and free Abelian topological groups.
Źródło:
Fundamenta Mathematicae; 1999, 159, 3; 195-218
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dichotomies pour les espaces de suites réelles
Autorzy:
Casevitz, Pierre
Powiązania:
https://bibliotekanauki.pl/articles/1205009.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Borel complexity
subspaces of real sequences
topology of subspaces of real sequences
Polishable spaces
dichotomy theorems
Borel equivalence relations
Opis:
There is a general conjecture, the dichotomy (C) about Borel equivalence relations E: (i) E is Borel reducible to the equivalence relation $E^X_G$ where X is a Polish space, and a Polish group acting continuously on X; or (ii) a canonical relation $E_1$ is Borel reducible to E. (C) is only proved for special cases as in [So].
 In this paper we make a contribution to the study of (C): a stronger conjecture is true for hereditary subspaces of the Polish space $ℝ^ω$ of real sequences, i.e., subspaces such that $[y=(y_n)_n ∈ X$ and ∀n, $|x_n| ≤ |y_n|] ⇒ x=(x_n)_n ∈ X$. If such an X is analytic as a subset of $ℝ^ω$, then either X is Polishable as a vector subspace, or X admits a subspace strongly isomorphic to the space $c_{00}$ of finite sequences, or to the space $ℓ_∞$ of bounded sequences.
 When X is Polishable, the metrics have a very simple form as in the case studied in [So], which allows us to study precisely the properties of those X's
Źródło:
Fundamenta Mathematicae; 2000, 165, 3; 249-284
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 157

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