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 is Cantor (arcwise) homogeneous iff X is a closed manifold of dimension at most 2.
@article{bwmeta1.element.bwnjournal-article-fmv142i2p139bwm, author = {Hanna Patkowska}, title = {On the LC1-spaces which are Cantor or arcwise homogeneous}, journal = {Fundamenta Mathematicae}, volume = {142}, year = {1993}, pages = {139-146}, zbl = {0846.54023}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv142i2p139bwm} }
Patkowska, Hanna. On the LC1-spaces which are Cantor or arcwise homogeneous. Fundamenta Mathematicae, Tome 142 (1993) pp. 139-146. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv142i2p139bwm/
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