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More on remainders close to metrizable spaces. (English) Zbl 1144.54001
The author continues his study of remainders in compactifications and generalized metrizability properties. He proves among other things that if \(X\) is a non-locally compact topological group, and \(bX\) is a compactification of \(X\) such that \(Y=bX\setminus X\) has a \(G_\delta\)-diagonal or a point-countable base, then both \(X\) and \(Y\) are separable and metrizable. A non-locally compact topological group may have a first countable remainder without being separable, which shows that the obtained results are close to being optimal. The author also notes that his results do not extend to paratopological groups.

54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
54B05 Subspaces in general topology
54D40 Remainders in general topology
Full Text: DOI
[1] Arhangel’skii, A.V., On a class of spaces containing all metric and all locally compact spaces, Mat. sb., Amer. math. soc. transl., 92, 109, 1-39, (1970), English transl.: · Zbl 0206.24804
[2] Arhangel’skii, A.V., Remainders in compactifications and generalized metrizability properties, Topology appl., 150, 79-90, (2005) · Zbl 1075.54012
[3] Engelking, R., General topology, (1977), PWN Warszawa
[4] Filippov, V.V., On feathered paracompacta, Dokl. akad. nauk SSSR, 178, 553-558, (1968), (in Russian) · Zbl 0167.21103
[5] Gruenhage, G., Generalized metric spaces, (), 423-501
[6] Henriksen, M.; Isbell, J.R., Some properties of compactifications, Duke math. J., 25, 83-106, (1958) · Zbl 0081.38604
[7] Roelke, W.; Dierolf, S., Uniform structures on topological groups and their quotients, (1981), McGraw-Hill New York
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