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Absolute countable compactness of products and topological groups. (English) Zbl 0976.54021
First, some closed subspaces of \(X\times Y\) are described that are absolutely countably compact (in the sense of M. V. Matveev [Topology Appl. 58, No. 1, 81-92 (1994; Zbl 0801.54021)]). Then it is proved that there is a separable, countably compact T\(_2\)-group that is not absolutely countably compact (if \(2^{\omega}<2^{\omega_1}\) and \(2^{\omega_1}\) is sequentially compact, then the group can be constructed sequentially compact).
MSC:
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54B10 Product spaces in general topology
54H11 Topological groups (topological aspects)
54D55 Sequential spaces
Citations:
Zbl 0801.54021
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