On abstract generalized topological spaces generated by the density type operators

Abstract

In the paper we concentrate on a generalized topological space generated by a density type operator on a measurable space. The properties of such generalized topological space are investigated. Moreover, the properties of nowhere dense sets, meager sets and compact sets in this generalized topological space are studied.

Keywords

• a generalized topological space
• separation axioms
• a nowhere dense set
• the lower density operator

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