Soft Closure Spaces

ON (L;M)-FUZZY CLOSURE SPACES

The aim of this paper is to introduce $(L,M)$-fuzzy closurestructure where $L$ and $M$ are strictly two-sided, commutativequantales. Firstly, we define $(L,M)$-fuzzy closure spaces and getsome relations between $(L,M)$-double fuzzy topological spaces and$(L,M)$-fuzzy closure spaces. Then, we introduce initial$(L,M)$-fuzzy closure structures and we prove that the category$(L,M)$-{bf FC} of $(L,M...

Violator spaces vs closure spaces

Violator Spaces were introduced by J. Matoušek et al. in 2008 as generalization of Linear Programming problems. Convex geometries were invented by Edelman and Jamison in 1985 as proper combinatorial abstractions of convexity. Convex geometries are defined by antiexchange closure operators. We investigate an interrelations between violator spaces and closure spaces and show that violator spaces ...

Soft Connected Spaces and Soft Paracompact Spaces

Linear v{C}ech closure spaces

In this paper, we introduce the concept of linear v{C}ech closure spaces and establish the properties of open sets in linear v{C}ech closure spaces (Lv{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $gamma$-open sets, sgc-dense sets and compact sets in Lv{C}CS. We also discuss the concept of relative v{C}ech closure operator, meet and pro...

On exponentiable soft topological spaces

An object $X$ of a category $mathbf{C}$ with finite limits is called exponentiable if the functor $-times X:mathbf{C}rightarrow mathbf{C}$ has a right adjoint. There are many characterizations of the exponentiable  spaces in the category $mathbf{Top}$ of topological spaces. Here, we study the exponentiable objects in the category $mathbf{STop}$ of soft topological spaces which is a generalizati...