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    Wyświetlanie 1-11 z 11
    Tytuł:
    Free spaces
    Autorzy:
    Song, Jian
    Tymchatyn, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/1205112.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    free space
    hereditarily indecomposable continuum
    polyhedron
    Opis:
    A space Y is called a free space if for each compactum X the set of maps with hereditarily indecomposable fibers is a dense $G_δ$-subset of C(X,Y), the space of all continuous functions of X to Y. Levin proved that the interval I and the real line ℝ are free. Krasinkiewicz independently proved that each n-dimensional manifold M (n ≥ 1) is free and the product of any space with a free space is free. He also raised a number of questions about the extent of the class of free spaces. In this paper we will answer most of those questions. We prove that each cone is free. We introduce the notion of a locally free space and prove that a locally free ANR is free. It follows that every polyhedron is free. Hence, 1-dimensional Peano continua, Menger manifolds and many hereditarily unicoherent continua are free. We also give examples that show some limits to the extent of the class of free spaces.
    Źródło:
    Fundamenta Mathematicae; 2000, 163, 3; 229-239
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Irreducibility of inverse limits on intervals
    Autorzy:
    Ryden, David
    Powiązania:
    https://bibliotekanauki.pl/articles/1205022.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    continuum
    irreducible
    inverse limit
    chainable
    triod
    unicoherent
    indecomposable
    absolutely terminal subcontinuum
    Opis:
    A procedure for obtaining points of irreducibility for an inverse limit on intervals is developed. In connection with this, the following are included. A semiatriodic continuum is defined to be a continuum that contains no triod with interior. Characterizations of semiatriodic and unicoherent continua are given, as well as necessary and sufficient conditions for a subcontinuum of a semiatriodic and unicoherent continuum M to lie within the interior of a proper subcontinuum of M.
    Źródło:
    Fundamenta Mathematicae; 2000, 165, 1; 29-53
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bing maps and finite-dimensional maps
    Autorzy:
    Levin, Michael
    Powiązania:
    https://bibliotekanauki.pl/articles/1205475.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    finite-dimensional maps
    hereditarily indecomposable continua
    Opis:
    Let X and Y be compacta and let f:X → Y be a k-dimensional map. In [5] Pasynkov stated that if Y is finite-dimensional then there exists a map $g : X → \mathbb{I}^k$ such that dim (f × g) = 0. The problem that we deal with in this note is whether or not the restriction on the dimension of Y in the Pasynkov theorem can be omitted. This problem is still open.
     Without assuming that Y is finite-dimensional Sternfeld [6] proved that there exists a map $g : X → \mathbb{I}^k$ such that dim (f × g) = 1. We improve this result of Sternfeld showing that there exists a map $g : X → mathbb{I}^{k+1}$ such that dim (f × g) =0. The last result is generalized to maps f with weakly infinite-dimensional fibers.
     Our proofs are based on so-called Bing maps. A compactum is said to be a Bing compactum if its compact connected subsets are all hereditarily indecomposable, and a map is said to be a Bing map if all its fibers are Bing compacta. Bing maps on finite-dimensional compacta were constructed by Brown [2]. We construct Bing maps for arbitrary compacta. Namely, we prove that for a compactum X the set of all Bing maps from X to $\mathbb{I}$ is a dense $G_δ$-subset of $C(X, \mathbb{I})$.
    Źródło:
    Fundamenta Mathematicae; 1996, 151, 1; 47-52
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hyperspaces of two-dimensional continua
    Autorzy:
    Levin, Michael
    Sternfeld, Yaki
    Powiązania:
    https://bibliotekanauki.pl/articles/1205496.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    hyperspaces
    hereditarily indecomposable continua
    one- and two-dimensional continua
    Opis:
    Let X be a compact metric space and let C(X) denote the space of subcontinua of X with the Hausdorff metric. It is proved that every two-dimensional continuum X contains, for every n ≥ 1, a one-dimensional subcontinuum $T_n$ with $dim C (T_n) ≥ n$. This implies that X contains a compact one-dimensional subset T with dim C (T) = ∞.
    Źródło:
    Fundamenta Mathematicae; 1996, 150, 1; 17-24
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Chaotic continua of (continuum-wise) expansive homeomorphisms and chaos in the sense of Li and Yorke
    Autorzy:
    Kato, Hisao
    Powiązania:
    https://bibliotekanauki.pl/articles/1208450.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    expansive homeomorphism
    continuum-wise expansive homeomorphism
    stable and unstable sets
    scrambled set
    chaotic in the sense of Li and Yorke
    independent
    indecomposable continuum
    Opis:
    A homeomorphism f : X → X of a compactum X is expansive (resp. continuum-wise expansive) if there is c > 0 such that if x, y ∈ X and x ≠ y (resp. if A is a nondegenerate subcontinuum of X), then there is n ∈ ℤ such that $d(f^n(x), f^n(y)) > c$ (resp. $diam f^n(A) > c$). We prove the following theorem: If f is a continuum-wise expansive homeomorphism of a compactum X and the covering dimension of X is positive (dim X > 0), then there exists a σ-chaotic continuum Z = Z(σ) of f (σ = s or σ = u), i.e. Z is a nondegenerate subcontinuum of X satisfying: (i) for each x ∈ Z, $V^σ(x; Z)$ is dense in Z, and (ii) there exists τ > 0 such that for each x ∈ Z and each neighborhood U of x in X, there is y ∈ U ∩ Z such that $lim inf_{n → ∞} d(f^n(x), f^n(y))$ ≥ τ if σ = s, and $lim inf_{n → ∞} d(f^{-n}(x), f^{-n}(y))$ ≥ τ if σ = u; in particular, $W^σ(x) ≠ W^σ(y)$. Here
      $V^s(x; Z) = {z ∈ Z|$ there is a subcontinuum A of Z such that
          x, z ∈ A and $lim_{n → ∞} diam f^n(A) = 0}$,
    $V^u(x; Z) = {z ∈ Z| there is a subcontinuum A of Z such that
          x, z ∈ A and $lim_{n → ∞} diam f^{-n}(A) = 0}$,
       $W^s(x) = {x' ∈ X|$ $lim_{n → ∞} d(f^n(x), f^n(x')) = 0}$, and
       $W^u(x) = {x' ∈ X|$ $lim_{n → ∞} d(f^{-n}(x), f^{-n}(x'))=0}$.
    As a corollary, if f is a continuum-wise expansive homeomorphism of a compactum X with dim X > 0 and Z is a σ-chaotic continuum of f, then for almost all Cantor sets C ⊂ Z, f or $f^{-1}$ is chaotic on C in the sense of Li and Yorke according as σ = s or u). Also, we prove that if f is a continuum-wise expansive homeomorphism of a compactum X with dim X > 0 and there is a finite family $\mathbb{F}$ of graphs such that X is $\mathbb{F}$-like, then each chaotic continuum of f is indecomposable. Note that every expansive homeomorphism is continuum-wise expansive.
    Źródło:
    Fundamenta Mathematicae; 1994, 145, 3; 261-279
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On indecomposability and composants of chaotic continua
    Autorzy:
    Kato, Hisao
    Powiązania:
    https://bibliotekanauki.pl/articles/1205482.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    expansive homeomorphism
    continuum-wise expansive homeomorphism
    indecomposable
    composant
    chaotic continuum
    plane compactum
    stable and unstable sets
    Opis:
    A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x,y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that $d(f^n(x),f^n(y)) > c$. A homeomorphism f: X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ ℤ such that $diami f^n(A) > c$. Clearly, every expansive homeomorphism is continuum-wise expansive, but the converse assertion is not true. In [6], we defined the notion of chaotic continua of homeomorphisms and proved the existence of chaotic continua of continuum-wise expansive homeomorphisms. Also, we studied indecomposability of chaotic continua. In this paper, we investigate further more properties of indecomposability of chaotic continua and their composants. In particular, we prove that if f:X → X is a continuum-wise expansive homeomorphism of a plane compactum $X ⊂ ℝ^2$ with dim X > 0, then there exists a σ-chaotic continuum Z (σ = s or u) of f such that Z is an indecomposable subcontinuum of X and for each z ∈ Z the composant c(z) of Z containing z coincides with the continuum-wise σ-stable set $V^σ(z;Z)$.
    Źródło:
    Fundamenta Mathematicae; 1996, 150, 3; 245-253
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Algorithm and program for finding minimal and quasi-minimal cuts in graphs
    Algorytm i program znajdowania minimalnych i quasi-minimalnych przekrojów grafu
    Autorzy:
    Grishkeyich, A.
    Piątek, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/268053.pdf
    Data publikacji:
    2008
    Wydawca:
    Politechnika Gdańska. Wydział Elektrotechniki i Automatyki
    Tematy:
    krata dystrybutywna
    przekrój nierozkladalny
    jeden, dwu, trzy elementowy przekrój
    distributive lattice
    indecomposable cut
    one-, two-, three- elements cut
    Opis:
    It was found, that the set of minimum cuts, separating two chosen vertices in graph, have the structure of distributive lattice. It was developed an effective procedure for finding the set of 1, 2 and 3 elements cuts in graph based on the consideration of distributive lattice of the set of minimum cuts. The procedure consists of first, the algorithm for finding indecomposable minimal cuts of distributive lattice. Second, algorithm for synthesis, using resulting subset from stage one, of the entire set of minimum cuts. The third, is the algorithm for describing the set of quasi-minimum (close to the minimum, next to minimum) cuts in the form of sum of distributive lattices of minimal cuts found for the modified function of weight. The computer program, implementing these algorithms, is presented with examples.
    Ustalono, że zbiór minimalnych przekrojów, rozdzielających dwa zadane wierzchołki grafu, z wprowadzonymi na i operacjami ma strukturę kraty dystrybutywnej. Opracowano skuteczną algorytmiczną procedurę znajdowania zbioru jed dwu i trzy elementowych przekrojów grafu bazującą na rozpatrzeniu dystrybutywnych krat zbioru minimalnych przekrojów grafu. Procedura składa się z, po pierwsze, algorytmu szukania nierozkładalnych minimalnych przekrojów Dystrybutywnej, po drugie, algorytmu syntezy po tym podzbiorze w kracie dystrybutywnej całego poszukiwanego zbioru minimalnych przekrojów i, po trzecie, algorytmu opisu zbioru quasi-minimalnych (bliskich do minimalnych, następnych po minimalnych) przekrojów w formie sumy krat dystrybutywnych minimalnych przekrojów, znalezionych dla zmodyfikowanej funkcji wagi. Przedstawiono zrealizowany program komputerowy i przedstawiono przykłady pracy programu.
    Źródło:
    Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej; 2008, 25; 49-52
    1425-5766
    2353-1290
    Pojawia się w:
    Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Open maps between Knaster continua
    Autorzy:
    Eberhart, Carl
    Fugate, J.
    Schumann, Shannon
    Powiązania:
    https://bibliotekanauki.pl/articles/1205180.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    continuum
    degree
    indecomposable
    (induced) open mapping
    semigroup
    approximating sequence
    Opis:
    We investigate the set of open maps from one Knaster continuum to another. A structure theorem for the semigroup of open induced maps on a Knaster continuum is obtained. Homeomorphisms which are not induced are constructed, and it is shown that the induced open maps are dense in the space of open maps between two Knaster continua. Results about the structure of the semigroup of open maps on a Knaster continuum are obtained and two questions about the structure are posed.
    Źródło:
    Fundamenta Mathematicae; 1999, 162, 2; 119-148
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Decomposition tree and indecomposable coverings
    Autorzy:
    Breiner, Andrew
    Deogun, Jitender
    Ille, Pierre
    Powiązania:
    https://bibliotekanauki.pl/articles/744120.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    interval
    indecomposable
    k-covering
    decomposition tree
    Opis:
    Let G = (V,A) be a directed graph. With any subset X of V is associated the directed subgraph G[X] = (X,A ∩ (X×X)) of G induced by X. A subset X of V is an interval of G provided that for a,b ∈ X and x ∈ V∖X, (a,x) ∈ A if and only if (b,x) ∈ A, and similarly for (x,a) and (x,b). For example ∅, V, and {x}, where x ∈ V, are intervals of G which are the trivial intervals. A directed graph is indecomposable if all its intervals are trivial. Given an integer k > 0, a directed graph G = (V,A) is called an indecomposable k-covering provided that for every subset X of V with |X| ≤ k, there exists a subset Y of V such that X ⊆ Y, G[Y] is indecomposable with |Y| ≥ 3. In this paper, the indecomposable k-covering directed graphs are characterized for any k > 0.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 1; 37-44
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The structure of atoms (hereditarily indecomposable continua)
    Autorzy:
    Ball, R.
    Hagler, J.
    Sternfeld, Yaki
    Powiązania:
    https://bibliotekanauki.pl/articles/1205357.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    atoms (hereditarily indecomposable continua)
    ultrametric spaces
    isometries
    lattices
    lattice isomorphism
    Opis:
    Let X be an atom (= hereditarily indecomposable continuum). Define a metric ϱ on X by letting $ϱ(x,y) = W(A_{xy})$ where $A_{x,y}$ is the (unique) minimal subcontinuum of X which contains x and y and W is a Whitney map on the set of subcontinua of X with W(X) = 1. We prove that ϱ is an ultrametric and the topology of (X,ϱ) is stronger than the original topology of X. The ϱ-closed balls C(x,r) = {y ∈ X:ϱ ( x,y) ≤ r} coincide with the subcontinua of X. (C(x,r) is the unique subcontinuum of X which contains x and has Whitney value r.) It is proved that for any two (nontrivial) atoms and any Whitney maps on them, the corresponding ultrametric spaces are isometric. This implies in particular that the combinatorial structure of subcontinua is identical in all atoms. The set M(X) of all monotone upper semicontinuous decompositions of X is a lattice when ordered by refinement. It is proved that for two atoms X and Y, M(X) is lattice isomorphic to M(Y) if and only if X is homeomorphic to Y.
    Źródło:
    Fundamenta Mathematicae; 1998, 156, 3; 261-278
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Statistical estimation of higher-order spectral densities by means of general tapering
    Autorzy:
    Baba Harra, M'hammed
    Powiązania:
    https://bibliotekanauki.pl/articles/1339110.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    shift-in-time
    higher-order spectral densities
    cumulant
    admissible values
    indecomposable partitions
    stochastic processes
    product moment
    tapering
    characteristic number
    Opis:
    Given a realization on a finite interval of a continuous-time stationary process, we construct estimators for higher order spectral densities. Tapering and shift-in-time methods are used to build estimators which are asymptotically unbiased and consistent for all admissible values of the argument. Asymptotic results for the fourth-order densities are given. Detailed attention is paid to the nth order case.
    Źródło:
    Applicationes Mathematicae; 1996-1997, 24, 4; 357-381
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-11 z 11

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