g*-closed sets and a new separation axiom in Alexandroff spaces

Pratulananda Das and Md. Mamun Ar. Rashid

E-mail:  pratulananda@yahoo.co.in
 

Abstract.
In this paper we introduce the concept of $g^{\ast }$-closed sets and
investigate some of its properties in the  spaces considered by
A.D. Alexandroff  [1] where only countable unions of open sets are required to
be open. We also introduce a new separation axiom called $T_{w}$-axiom in
the Alexandroff spaces with the help of $g^{\ast}$-closed sets and
investigate some of its consequences.

AMSclassification. 54A05, 54C08, 54D10

Keywords.  Space,  $g^{\ast}$-closed sets, $g^{\ast}$-open sets, $T_{w}$-space.