Extreme point axioms for closure spaces

Higher Separation Axioms in Generalized Closure Spaces

The hierarchy of separation axioms that is familiar from topological spaces generalizes to spaces with an isotone and expansive closure function. Neither additivity nor idempotence of the closure function must be assumed.

BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...

Soft semi separation axioms and some types of soft functions

Shabir and Naz in [25] introduced the notion of soft topological spaces. They defined basic notions of soft topological spaces such as open soft sets, closed soft sets, soft subspaces, soft closure, soft nbd of a soft point, soft separation axioms, soft regular spaces, soft normal spaces and they established their several properties. Min in [19] investigated some properties of such soft separat...

The Urysohn, completely Hausdorff and completely regular axioms in $L$-fuzzy topological spaces

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

Some separation axioms via modified θ-open sets