On the LC1-spaces which are Cantor or arcwise homogeneous

Hanna Patkowska

ArticleOriginal scientific text

Title

On the LC1-spaces which are Cantor or arcwise homogeneous

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Department of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Abstract

A space X containing a Cantor set (an arc) is Cantor (arcwise) homogeneous} iff 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 \in L C^{1}

is Cantor (arcwise) homogeneous iff X is a closed manifold of dimension at most 2.

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm142/fm14223.pdf

Title

On the LC1-spaces which are Cantor or arcwise homogeneous

Affiliations

Abstract

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