Open sets and Locally Sierpinski spaces on To?Alexandroff spaces

The aim of this paper is to continue the study of  T_o?Alexandroff spaces, a class of topological spaces which lies strictly between classes of Alexandroff spaces and locally finite spaces.  We study b-open sets and prove that BO(X)=SO(X) in Artinian T_o?Alexandroff spaces.  After that, we investigate locally Sierpinski spaces.  Each locally Sierpinski space is submaximal T_o?Alexandroff space.  The converse is not true. 

In this paper we will introduce a sufficient condition for a submaximal T_o?Alexandroff space to be locally Sierpinski space.

Keywords: Alexandroff spaces, Artinian T_o?Alexandroff spaces, b-open sets, semi-open sets, locally Sierpinski spaces, submaximal.

2000 Mathematics Subject Classification. Primary  54D10, 54F05; Secondary 54F65.