Some properties of the topology of \(\alpha\) -sets. (English) Zbl 0546.54003

Andrijević, Dimitrije

Mat. Vesn. 36, 1-10 (1984).

A subset B of a topological space (X,\({\mathcal T})\) is called an \(\alpha\) - set if \(B\subset int(cl(int B))\). The family \({\mathcal T}^{\alpha}\) of all \(\alpha\) -sets in (X,\({\mathcal T})\) is a topology on X. The author considers some properties of this topology \({\mathcal T}^{\alpha}\), and how these relate to the topology \({\mathcal T}\).

Reviewer: I.L.Reilly

MSC:

54A10	Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54A05	Topological spaces and generalizations (closure spaces, etc.)

Keywords:

semi-open set; \(\alpha\) -set