Mazurkiewicz manifolds and homogeneity
classification
🧮 math.GN
math.GT
keywords
locallyappliescompactconnecteddifferentdimensiondimensionsfinite
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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.
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