Displaying similar documents to “Menger curves in Peano continua”

On the LC1-spaces which are Cantor or arcwise homogeneous

Hanna Patkowska (1993)

Fundamenta Mathematicae

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A space X containing a Cantor set (an arc) is Cantor (arcwise) homogeneousiff for any two Cantor sets (arcs) A,B ⊂ X there is an autohomeomorphism h of X such that h(A)=B. It is proved that a continuum (an arcwise connected continuum) X such that either dim X=1 or X ∈ L C 1 is Cantor (arcwise) homogeneous iff X is a closed manifold of dimension at most 2.

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.