×

On submaximal and quasi-submaximal spaces. (English) Zbl 1210.54006

Summary: The purpose of this paper is to study some properties of quasi-submaximal spaces and related examples. More precisely, we prove that if \(X\) is a quasi-submaximal and nodec space, then \(X\) is submaximal. As properties of quasi-submaximality, we show that if \(X\) is a quasi-submaximal space, then (a) for every dense \(D\subset X\), \(\text{Int}(D)\) is dense in \(X\), and (b) there are no disjoint dense subsets.
Also, we illustrate some basic facts and examples giving the relationships among the properties mentioned in this paper.

MSC:

54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54F65 Topological characterizations of particular spaces
PDFBibTeX XMLCite
Full Text: DOI Link