Abstract:An $\alpha $-space is a topological space in which the topology is generated by the family of all $\alpha $-sets (see [N]). In this paper, minimal-$\alpha \Cal P$-spaces (where $\Cal P$ denotes several separation axioms) are investigated. Some new characterizations of $\alpha $-spaces are also obtained.
Keywords: $\alpha $-space, $\alpha T_i$-space, minimal-$\alpha T_i$ space, $T_2$-closed space, minimal-$T_2$ space, $\psi $-space
AMS Subject Classification: Primary 54A10, 54D25; Secondary 54A05, 54D80