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Keywords:
space; $g^{\ast }$-closed sets; $g^{\ast }$-open sets; $T_{w}$-space
space; $g^{\ast }$-closed sets; $g^{\ast }$-open sets; $T_{w}$-space
Summary:
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.
References:
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