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On a compactification of the homeomorphism group of the pseudo-arc

Kazuhiro Kawamura (1991)

Colloquium Mathematicae

A continuum means a compact connected metric space. For a continuum X, H(X) denotes the space of all homeomorphisms of X with the compact-open topology. It is well known that H(X) is a completely metrizable, separable topological group. J. Kennedy [8] considered a compactification of H(X) and studied its properties when X has various types of homogeneity. In this paper we are concerned with the compactification $G_{P}$ of the homeomorphism group of the pseudo-arc P, which is obtained by the method of...

On a metrization of the hyperspace of a metric space

Karol Borsuk (1977)

Fundamenta Mathematicae

On admissible Whitney maps

Hisao Kato (1988)

Colloquium Mathematicae

On approximation of multifunctions with respect to the Vietoris topology

Andrzej Spakowski (1988)

Acta Universitatis Carolinae. Mathematica et Physica

On connectivity properties of bitopological hyperspaces

M. Mršević (1980)

Matematički Vesnik

On connectivity properties of hyperspaces of $R_{0}$ spaces

M. Mršević (1979)

Matematički Vesnik

On ℳ-contractibility

Takemi Mizokami (1981)

Colloquium Mathematicae

On convex metric spaces V

R. Duda (1970)

Fundamenta Mathematicae

On generalized whitney mappings

M. Van de Vel (1984)

Compositio Mathematica

On Hausdorff intrinsic metric.

Sosov, E.N. (2001)

Lobachevskii Journal of Mathematics

On hit-and-miss hyperspace topologies

Gerald Beer, Robert K. Tamaki (1993)

Commentationes Mathematicae Universitatis Carolinae

The Vietoris topology and Fell topologies on the closed subsets of a Hausdorff uniform space are prototypes for hit-and-miss hyperspace topologies, having as a subbase all closed sets that hit a variable open set, plus all closed sets that miss (= fail to intersect) a variable closed set belonging to a prescribed family $Δ$ of closed sets. In the case of the Fell topology, where $Δ$ consists of the compact sets, a closed set $A$ misses a member $B$ of $Δ$ if and only if $A$ is far from $B$ in a uniform sense....

On indecomposability and composants of chaotic continua

Hisao Kato (1996)

Fundamenta Mathematicae

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 $d i a m i f^{n} (A) > c$ . 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...

On local 1-connectedness of Whitney continua

Hisao Kato (1988)

Fundamenta Mathematicae

On Mazurkiewicz sets

Marta N. Charatonik, Włodzimierz J. Charatonik (2000)

Commentationes Mathematicae Universitatis Carolinae

A Mazurkiewicz set $M$ is a subset of a plane with the property that each straight line intersects $M$ in exactly two points. We modify the original construction to obtain a Mazurkiewicz set which does not contain vertices of an equilateral triangle or a square. This answers some questions by L.D. Loveland and S.M. Loveland. We also use similar methods to construct a bounded noncompact, nonconnected generalized Mazurkiewicz set.

On metrization of hyperspaces

Flachsmeyer, Jürgen (1977)

Abstracta. 5th Winter School on Abstract Analysis

On multifunctions with closed graphs

D. Holý (2001)

Mathematica Bohemica

The set of points of upper semicontinuity of multi-valued mappings with a closed graph is studied. A topology on the space of multi-valued mappings with a closed graph is introduced.

On Pixley-Roy hyperspaces

Hajnal, A. (1981)

Abstracta. 9th Winter School on Abstract Analysis

On reflexive closed set lattices

Zhongqiang Yang, Dong Sheng Zhao (2010)

Commentationes Mathematicae Universitatis Carolinae

For a topological space $X$ , let $S (X)$ denote the set of all closed subsets in $X$ , and let $C (X)$ denote the set of all continuous maps $f : X \to X$ . A family $𝒜 \subseteq S (X)$ is called reflexive if there exists $𝒞 \subseteq C (X)$ such that $𝒜 = {A \in S (X) : f (A) \subseteq A$ for every $f \in 𝒞}$ . Every reflexive family of closed sets in space $X$ forms a sub complete lattice of the lattice of all closed sets in $X$ . In this paper, we continue to study the reflexive families of closed sets in various types of topological spaces. More necessary and sufficient conditions for certain families of closed...

On shape of hyperspaces

Y. Kodama, S. Spież, T. Watanabe (1978)

Fundamenta Mathematicae

On subspaces of the Pixley-Roy example

Szymon Plewik (1981)

Colloquium Mathematicae

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