Displaying similar documents to “On the LC1-spaces which are Cantor or arcwise homogeneous”

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

Kazuhiro Kawamura (1991)

Colloquium Mathematicae

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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...

Strongly chaotic dendrites

J. Charatonik, W. Charatonik (1996)

Colloquium Mathematicae

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The concept of a strongly chaotic space is introduced, and its relations to chaotic, rigid and strongly rigid spaces are studied. Some sufficient as well as necessary conditions are shown for a dendrite to be strongly chaotic.

On self-homeomorphic dendrites

Janusz Jerzy Charatonik, Paweł Krupski (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that for every numbers m 1 , m 2 ∈ { 3 , ⋯ , ω } there is a strongly self-homeomorphic dendrite which is not pointwise self-homeomorphic. The set of all points at which the dendrite is pointwise self-homeomorphic is characterized. A general method of constructing a large family of dendrites with the same property is presented.

On the disjoint (0,N)-cells property for homogeneous ANR's

Paweł Krupski (1993)

Colloquium Mathematicae

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A metric space (X,ϱ) satisfies the disjoint (0,n)-cells property provided for each point x ∈ X, any map f of the n-cell B n into X and for each ε > 0 there exist a point y ∈ X and a map g : B n → X such that ϱ(x,y) < ε, ϱ ^ ( f , g ) < ε and y ∉ g ( B n ) . It is proved that each homogeneous locally compact ANR of dimension >2 has the disjoint (0,2)-cells property. If dimX = n > 0, X has the disjoint (0,n-1)-cells property and X is a locally compact L C n - 1 -space then local homologies satisfy H k ( X , X - x ) = 0 for k < n and Hn(X,X-x)...