Mathematics Commons^™

Generalized Homogeneity Of Finite And Of Countable Topological Spaces, J. J. Charatonik, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

Finite and countable topological spaces are investigated which are homogeneous, homogeneous with respect to open mappings or with respect to continuous ones. It is shown that for finite spaces all three concepts of homogeneity coincide, while for countable or for uncountable ones they are distinct. Some characterization of countable spaces that are homogeneous in either sense are found for the metric setting.