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Selections and approaching points in products

Valentin Gutev (2016)

Commentationes Mathematicae Universitatis Carolinae

The present paper aims to furnish simple proofs of some recent results about selections on product spaces obtained by García-Ferreira, Miyazaki and Nogura. The topic is discussed in the framework of a result of Katětov about complete normality of products. Also, some applications for products with a countably compact factor are demonstrated as well.

Skula spaces

Alan S. Dow, Stephen W. Watson (1990)

Commentationes Mathematicae Universitatis Carolinae

Spaces in which compact subsets are closed and the lattice of T 1 -topologies on a set

Ofelia Teresa Alas, Richard Gordon Wilson (2002)

Commentationes Mathematicae Universitatis Carolinae

We obtain some new properties of the class of KC-spaces, that is, those topological spaces in which compact sets are closed. The results are used to generalize theorems of Anderson [1] and Steiner and Steiner [12] concerning complementation in the lattice of T 1 -topologies on a set X .

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