Abstract In the context of partially ordered vector spaces one encounters different sorts order convergence and topologies. This article investigates these notions their relations. particular, we study relate topology presented by Floyd, Vulikh Dobbertin, bound studied Namioka concept given in works Abramovich, Sirotkin, Wolk Vulikh. We prove that considered topologies disagree for all infinite...

In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $top$-filters, namely $top$-convergence spaces, and show the category of $top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of$top$-convergence spaces and that of strong $L$-topological spaces is establish...

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

We present a topological minimax theorem (Theorem 2.2). The topological assumptions on the spaces involved are somewhat weaker than those usually found in the literature. Even when reinterpreted in the convex setting of topological vector spaces, our theorem yields nonnegligible improvements, for example, of the Passy–Prisman theorem and consequently of the Sion theorem, contrary to most result...

We study the validity of two basic results of the classical theory of topological vector spaces in the context of topological modules.

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...

In this note, we establish and improve some results on fixed point theory in topological vector spaces. As a generalization of contraction maps, the concept of quasi contraction multivalued maps on a topological vector space will be defined. Further, it is shown that a quasi contraction and closed multivalued map on a topological vector space has a unique fixed point if it is bounded value.