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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.

##### MSC:
 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 54B05 Subspaces in general topology 54D40 Remainders in general topology
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##### References:
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