On the LC1-spaces which are Cantor or arcwise homogeneous
Volume 142 / 1993
Fundamenta Mathematicae 142 (1993), 139-146 DOI: 10.4064/fm-142-2-139-146
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 $X ∈ LC^1$ is Cantor (arcwise) homogeneous iff X is a closed manifold of dimension at most 2.