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.
J. J. Charatonik and W. J. Charatonik, "Generalized Homogeneity of Finite and of Countable Topological Spaces," Rocky Mountain Journal of Mathematics, Rocky Mountain Mathematics Consortium, Jan 1988.
The definitive version is available at https://doi.org/10.1216/RMJ-1988-18-1-195
Mathematics and Statistics
Keywords and Phrases
continuous mapping; countable; finite; homogeneous; metric space; open mapping; regular space
International Standard Serial Number (ISSN)
Article - Journal
© 1988 Rocky Mountain Mathematics Consortium, All rights reserved.