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    Wyświetlanie 1-5 z 5
    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:
    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:
    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:
    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:
    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
      Wyświetlanie 1-5 z 5

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