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...

The purpose of the present article is to introduce notion (Λ, s)-closed sets. Especially, some properties generalized sets are obtained. Several characterizations low separation axioms given. Characterizations s)-extremally disconnected spaces investigated. Furthermore, almost s)-continuous functions discussed.

We extend dynamic logic of propositional assignments by adding an operator parallel composition that is inspired separation logics. provide axiomatization via reduction axioms, thereby establishing decidability. also prove the complexity both model checking and satisfiability problem stay in PSPACE.

By using the notion of m-spaces, we establish the unified theory for several variations of separation axioms quasi T0, quasi T1 and quasi T2 in bitopological spaces.

The authors characterize the notion of quasi coincident in texture spaces and study the generalization of fuzzy quasi separation axioms defined by [12] to the ditopological texture 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...

Separation Algebras serve as models of Separation Logics; Share Accounting allows reasoning about concurrent-read/exclusive-write resources in Separation Logic. In designing a Concurrent Separation Logic and in mechanizing proofs of its soundness, we found previous axiomatizations of separation algebras and previous systems of share accounting to be useful but imperfect. We adjust the axioms of...