On some weaker forms of alexandroff spaces

الملخص EN

Alexandroff spaces are the topological spaces in which each element is contained in a smallest open set or equivalently the spaces where arbitrary intersections of open sets are open.

In this paper we introduce and study two weaker concepts of Alexandroff spaces, namely generalized Alexandroff and semi-Alexandroff spaces.

In ri/2-spaces the concepts of Alexandroff and g-Alexandroff spaces coincide, while the class of semi-Alexandroff spaces is properly placed between the classes of Alexandroff and /''-spaces.

Math.

Subject Classification: Primary: 54G05, 54G10 Secondary: 54H05, 54G99