Abstract: | In this article we introduce the notions of p* - T1 space, p* - T2 , p*-regular space and p*-Urysohn space, an analogue of the classical notion of T1 space, T2 space, regular space and Urysohn space respectively, where the role of open sets (resp., of the corresponding closure operator Cl) is played by p-open sets (resp., by the corresponding p-closure operator Cl p ). It is seen that the notion of p*-Urysohn space is stronger than each of the notion Urysohn space, pre-Urysohn space, p-Urysohn space and weakly Hausdorff space. The notion of ordered pair of pre-open sets in a topological space is introduced along with and some important and interesting results have been obtained. Using p-open sets, one can introduce and study various notions in
topological spaces. |
