Characteristics of penta-open sets in penta topological spaces

Document Type : Research Paper


1 Department of mathematics, College of education for women, Tikrit University, Iraq.

2 Department of Mathematics, College of Education for Pure Sciences, Tikrit University, Iraq.

3 Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Iraq.


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.