A unified theory of generalized closed sets in weak structures
The authors continue the investigation of generalised topological spaces. Here it is no longer requested that the members of a generalised topology \(w\) are closed under intersection or union. In general, \(w\) does not replace the topology but is an additional structure added to a topology \(\tau\) on a set \(X\). For example the authors study when in a topological space \((X,\tau)\) the closed sets can be separated by disjoint \(w\)-open sets for a suitable weak structure \(w\). Prior work had considered special cases of \(w\), say the closures of open sets or the interiors of closed sets. The authors provide a large collection of results in various settings on the relation of normal closure in \((X,\tau)\) with generalised closure (induced by the weak structure) and so on.
scientific article; zbMATH DE number 6151033
scientific article