On \(b\)-open setes. (English) Zbl 0885.54002

Andrijević, Dimitrije

Mat. Vesn. 48, No. 1-2, 59-64 (1996).

A subset \(S\subset X\) is called \(b\)-open if \(S\subset\text{cl int} S\cup\text{int cl} S\). The class \(BO(X)\) of \(b\)-open sets in topological space \(X\) is studied. Some of the results are as follows.
The inclusions \(PO(X)\cup SO(X)\subset BO(X)\subset SPO(X)\) cannot be replaced by equalities. The class \(BO(X)\) generates the same topology as the class \(PO(X)\).

Reviewer: Dušan Adnadjević (Beograd)

MSC:

54A10

Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)

Keywords:

\(\alpha\)-sets; semi-open set; preopen set; semi-preopen set; \(b\)-open set; \(\mathcal T_ b\)-topology