In this paper by using rgα−open sets I define almost rgα−normality and mild rgα−normality also we continue the study of further properties of rgα−normality. We show that these three axioms are regular open hereditary. I also define the class of almost rgα−irresolute mappings and show that rgα−normality is invariant under almost rgα−irresolute M-rgα−open continuous surjection.

In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.

In this paper examples are given to show that s-regular and s-normal are independent; that s-normal, and s-regular are not semi topological properties; and that (S(X),E(X)) need not be I even if (X,T) is compact, s-normal, s-regular, semi-T2, and T0. Also, it is shown that for each space (X,T), (S(X) ,E(X)), (S(XO) ,E(Xo)), and (S(Xs0) ,E(Xs0)) are homeomorphic, where (X0, Q(X0)) is the T0-iden...

Let $X$ be an infinite set, equipped with a topology $tau$. In this paper we studied the relationship between $tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.