e-Open sets and separation axioms in fuzzifying topology

Some separation axioms via modified θ-open sets

On bD-Sets and Associated Separation Axioms

α- separation axioms based on Lukasiewicz logic

In the present paper, we introduce topological notions defined by means of α-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). We introduce T 0 −, T 1 −, T 2 (αHausdorff)-, T 3 (α-regular)and T 4 (αnormal)-separation axioms. Furthermore, the R 0− and R 1− separation axioms are studied and their relations with the T 1 − ...

On invariant sets topology

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

Generated topology on infinite sets by ultrafilters

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.