Mazurkiewicz manifolds and homogeneity

Abstract

It is proved that no region of a homogeneous locally compact, locally connected metric space can be cut by an $F_{\sigma }$-subset of a "smaller" dimension. The result applies to different finite or infinite topological dimensions of metrizable spaces.

5 pages

References in corpus (1)

• Generalized Cantor manifolds and homogeneity

Cited by in corpus (1)

• Alexandroff type manifolds and homology manifolds