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...

Let X and Y be completely regular spaces and E and F be Hausdorff topological vector spaces. We call a linear map T from a subspace of C(X, E) into C(Y, F ) a Banach-Stone map if it has the form Tf(y) = Sy(f(h(y)) for a family of linear operators Sy : E → F , y ∈ Y , and a function h : Y → X. In this paper, we consider maps having the property: (Z) ∩ki=1 Z(fi) 6= ∅ ⇐⇒ ∩ k i=1Z(Tfi) 6= ∅, where ...

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...

It is proved that there exist complemented subspaces of countable topo-logical products (locally convex direct sums) of Banach spaces which cannot be represented as topological products (locally convex direct sums) of Banach spaces The problem of description of complemented subspaces of a given locally convex space is one of the general problems of structure theory of locally convex spaces. In ...

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...