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...

The original definition of a topological space given by Hausdorff used neighborhood systems. Lattice-valued maps appear in this context when you identify a topology with a monoid in the Kleisli category of the filter monad on SET. H?hle’s notion of a lattice-valued topology [2] uses the same idea and it’s inspired in the classical lattice-valued topologies. Ltopological spaces are motivated by ...

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...