## 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

### Keywords:

absolutely countably compact spaces; topological group

Zbl 0801.54021
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