Mazurkiewicz manifolds and homogeneity

2009/01/09 by P. Krupski, Krupski, P., V. Valov +1
Mathematics · #54F45 (Primary) #55M10(Secondary) #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #math.GN #math.GT #msc:54F45

paper · pdf · doi:10.48550/arxiv.0901.1329

5 pages

arxiv created 2009/01/09 · arxiv updated 2009/12/01

Abstract

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

Related

• Alexandroff type manifolds and homology manifolds
• Generalized Cantor manifolds and homogeneity
• Discrete homogeneity and ends of manifolds
• Separation of homogeneous connected locally compact spaces
• Homogeneous spaces not separated by arcs