On $s$-closedness and $\Cal S$-closedness in topological spaces

Zbigniew Duszyński

On $s$ -closedness and $S$ -closedness in topological spaces

Authors

Zbigniew Duszyński Institute of Mathematics, Casimirus the Great University, Pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland Author

Keywords:

α

-open, semi-open, preopen, semi-preopen, semi-regular sets,

s

-closed,

S

-closed

Subjects:

54G99

Abstract

Some properties of sets $s$ -closed or $S$ -closedrelative to a space, and $s$ -closed or $S$ -closed subspaces, areobtained. Relationships between some of them are indicated. Newcharacterizations of Hausdorff spaces in terms of $s$ -closednessand $α$ -compactness relative to a space, are obtained.