Search

Based on the abstract version of the Smital property, we introduce an operator $DS$. We use it to characterise the class of semitopological abelian groups, for which addition is a quasicontinuous operation. [ABSTRACT FROM AUTHOR]

We consider a special kind of structure resolvability and irresolvability for measurable spaces and discuss analogues of the criteria for topological resolvability and irresolvability. [ABSTRACT FROM AUTHOR]

We demonstrate that many properties of topological spaces connected with the notion of resolvability are preserved by the relation of similarity between topologies. Moreover, many of them can be characterised by the properties of the algebra of sets with nowhere dense boundary and the ideal of nowhere dense sets. We use these results to investigate whether a given pair of an algebra and an ideal is topological. [ABSTRACT FROM PUBLISHER]