ON FILTER EXPANSION OF TOPOLOGIES

Abstract


 
 
 The lower separation axioms $T_i$, ($i \in \{0, 1, 2\}$) are obviously preserved under topology expansions. This fact is not generally valid for higher separation axioms as well as for recent sorts of separation such as $T_R$, $R_0$, $R_1$ and semi-$R_i$, ($i \in \{0, 1\}$). The purpose of the present work is to investigate preservation of these recent separation properties under filter expansion of topologies. Also, we study the effect of filter expansions on the concept $s$-essentially $T_i$- spaces, ($i \in \{0, 1\}$).