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On the LC1-spaces which are Cantor or arcwise homogeneous

Hanna Patkowska — 1993

Fundamenta Mathematicae

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.

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