On some weaker forms of Alexandroff spaces by Francisco G. Arenas, Julian Dontchev and Maximilian Ganster

Topology Atlas Document # paba-01 | Production Editor: S. Chastain

On some weaker forms of Alexandroff spaces

Francisco G. Arenas, Julian Dontchev and Maximilian Ganster

Topology Atlas Preprint # 120

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 T_1/2-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 P^'-spaces.

Mathematics Subject Classification: 54G05, 54G10 (54H05, 54G99)
Keywords: P-space, P'-space, Alexandroff-space, semi-open, g-open, g-closed

Date received: February 18, 1996.
Date published: May 5, 1996.