Absolute countable compactness of products and topological groups. (English) Zbl 0976.54021

Song, Y.-K.

Commentat. Math. Univ. Carol. 40, No. 2, 367-372 (1999).

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).

Reviewer: Miroslav Hušek (Praha)

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

Citations:

Zbl 0801.54021