In this work, we introduce the notion of generalized ω-closed set in a soft topological space with a soft weak structure. And some basic properties of this new class are investigated by using the concept of weak structure. Moreover, we study soft ω-T 1 2 -spaces defined by soft gω-closed sets and study some properties of it by using gω-open sets.
The class of ω-closed subsets of a space (X, τ) was defined to introduce ω-closed functions. The purpose of this paper to introduce the notion of ω-local functions and to give some of its basic properties in an ideal topological space. Moreover, we define and investigate the ω-compatible spaces. MSC 2010. 54A05, 54C10.
In this paper we introduce and investigate the notions of a new class of generalized semiclosed functions and a class of semi-generalized closed functions in bitopological spaces. We study the further properties of ij-generalized semi closed and ij-semi-generalized closed sets. Applying of these concepts of sets, we introduce and study two new spaces, namely pairwise generalized s-regular and pairwise s-normal spaces.
We prove the existence and uniqueness of classical and strong solutions of a fractional semilinear evolution equation using the method of a semigroup and the Banach fixed theorem.
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