A Study of New Type of Minimal Open and Maximal Closed Sets

Halgwrd Mohammed Darwesh

Abstract

In this paper, we show that the notions of maximal feebly open and minimal feebly closed sets are nothing except  maximal $\alpha$-open and minimal $\alpha$-closed sets. Further, we show that the ideas of minimal feebly open and maximal feebly closed sets coincide with minimal open and maximal closed sets. Therefore, we introduce new notions of minimal open and maximal closed sets, namely $f$-minimal open and $f$-maximal closed sets, some of their properties, characterizations, and relationships established.