Inner structure appeared in the literature of topological vector spaces as a tool to characterize extremal convex sets. For instance, recent years, inner has been used provide solution The Faceless Problem and finest locally topology on real space. This manuscript goes one step further by settling bases for studying non-convex In first place, we observe that well behaviour sets with respect doe...

In this paper, the notion of fuzzy semicompactness degrees isintroduced in $L$-fuzzy topological spaces by means of theimplication operation of $L$. Characterizations of fuzzysemicompactness degrees in $L$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

There are more and more papers dealing with situations where probabilistic features occur together with ordinary nondeterminism. Based on the PhD thesis by R. Tix [18], domain theoretical tools for combining probability with nondeterminism were developped in [19]. A motivating situation was the semantics of an imperative language with both probabilistic and nondeterministic choice as considered...

This paper provides necessary and sufficient conditions for the existence of pure strategy Nash equilibria by replacing the assumptions concerning continuity and quasiconcavity with a unique condition, passing strategy space from topological vector spaces to arbitrary topological spaces. Preferences may also be nontotal/nontransitive, discontinuous, nonconvex, or nonmonotonic. We define a singl...

In this paper, the concepts of derived sets and derived operators are generalized to $(L, M)$-fuzzy topological spaces and their characterizations are given.What is more, it is shown that the category of stratified $(L, M)$-fuzzy topological spaces,the category of stratified $(L, M)$-fuzzy closure spaces and the category of stratified $(L, M)$-fuzzy quasi-neighborhood spaces are all isomorphic ...