Abstract

Generalizations of openness, such as semi-open, preopen, semi-pre-open, $\alpha$-open, etc\. are important in topological spaces and in particular in topological spaces on which ideals are defined. $\alpha$-equivalent topologies and $*$-equivalent topologies with respect to an ideal have some common properties. Relations between these aforementioned notions of openness are investigated within the framework of $\alpha$-equivalence and $*$-equivalence.

Keywords: $\alpha$-equivalent topologies; $*$-equivalent topologies; semi-open sets, preopen sets, semi-pre-open sets, $\alpha$-open sets.

MSC: 54A05, 54A10, 54C08, 54C10

Pages:  85$-$95     

Volume  59 ,  Issue  3 ,  2007