In this manuscript, we continue to study the hypersoft topological space (for short, HSTS) by presenting (HS) separation axioms, called HS Ti-spaces for i = 0, 1, 2, 3, 4. The notions of regular and normal spaces are explained in detail. We discuss connections between them present numerous examples help clarify interconnections different types these spaces. point out that Ti-axioms imply Ti?1 w...

nets, useful topological tools, used to generalize certainconcepts that may only be general enough in the context of metricspaces. in this work we introduce this concept in an $s$-poset, aposet with an action of a posemigroup $s$ on it whichis a very useful structure in computer sciences and interestingfor mathematicians, and give the the concept of $s$-net. using $s$-nets and itsconvergency we...

in this paper‎, ‎we introduce a new model of point free topology‎ ‎for point-set topology‎. ‎we study the basic concepts in this‎ ‎structure and will find that it is naturally close to point-set‎ ‎topology‎.‎