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

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