Linearly S-closed spaces

Gunjan Singh ; A R Prasannan

Filomat, Tome 36 (2022) no. 20, p. 6841

Résumé

We introduce the class of linearly S-closed spaces as a proper subclass of linearly H-closed spaces. This property lies between S-closedness and countable S-closedness. A space is called linearly S-closed if and only if any semi-open chain cover posses a member dense in the space. It is shown that in the class of extremally disconnected spaces the class of linearly H-closed spaces and linearly S-closed spaces coincide. We gave characterizations of these spaces in terms of s-accumulation points of chain filter bases and complete s-accumulation points of families of open subsets. While regular S-closed spaces are compact there is a non compact, regular, linearly S-closed space. It is shown that a Hausdorff, first countable, linearly S-closed space is extremally disconnected. Moreover, in the class of first countable, regular, compact spaces the notions of S-closedness, linearly S-closedness and extremally disconnectedness are equivalent. Some cardinality bounds for this class of spaces are obtained. Several examples are provided to illustrate our results.

Détail

DOI : 10.2298/FIL2220841S

Classification : 54D20, 54F65, 54G05
Keywords: Feebly compact, H-closed, quasi H-closed, linearly H-closed, S-closed, countably S-closed, lob, extremally disconnected, ccc