Characteristics of penta-open sets in penta topological spaces

The aim of the presented study is to introduce and verify two new spaces called \mathcal{P}\_ compactness and  \mathcal{P}\_connectedness using \mathcal{P}\_open sets and some of their properties. Moreover, we study the relationship between these spaces. Another purpose of this study is to examine a new form of separation axioms, by using \mathcal{P}\_open set namely T_{\mathcal{P}i}-spaces where (i=0,1,2). The pertinence between them has been discussed and several features of these spaces are demonstrated as well.

Characteristics of penta-open sets in penta topological spaces Keywords:

Penta Topological Space , mathcal{P}_irresolute function , mathcal{P}_compactness , locally mathcal{P}_compact , mathcal{P}_Connectedness , mathcal{P}_separated , strongly mathcal{P}_connected , T_{mathcal{P}i}-space