In this article we established the concept of multi-continuity in minimal structure spaces (in short $\mathscr{M}$ space) and notion product space multiset topological space. Continuity between $\mathscr{M}$-space, generalized topology ideal spaces. We have investigated some basic properties $\mathscr{M}$–continuity space, such as composition $\mathscr{M}$–continuous functions, functions etc.

The concept of a topology for the fundamental group appears to have originated with Hurewicz (1935), but it has been actively studied only for the last ten years. The classical fundamental group of a pointed topological space X naturally inherits the quotient topology from the space of based loops in X endowed with the compact-open topology. The resulting space, called the topological fundament...

n this paper, we consider continuity properties(especially, regularity, also viewed as an approximation property) for $%mathcal{P}_{0}(X)$-valued set multifunctions ($X$ being a linear,topological space), in order to obtain Egoroff and Lusin type theorems forset multifunctions in the Vietoris hypertopology. Some mathematicalapplications are established and several physical implications of thema...

This paper is concerned with the study of fuzzy dynamical systems. Let (XM ) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map dened on X. We introduce the various fuzzy shad- owing and fuzzy topological transitivity on a fuzzy discrete dynamical systems. Some relations between this notions have been proved.

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.

We are here dealing with the problem of space layout planning. We present an approach based on an intermediate topological level with dynamic space ordering (dso) heuristics. Our software ARCHiPLAN proceeds through a number of steps. First, all the topologically different solutions, without presuming any precise dimension, are enumerated. Next, we may evolve in this topological solution space, ...

Definition 1 (compare [2,5,8]) A topological space is called a KC-space provided that each compact set is closed. A topological space is called a U S-space provided that each convergent sequence has a unique limit. Remark 1 Each Hausdorff space (= T 2-space) is a KC-space, each KC-space is a U S-space and each U S-space is a T 1-space (that is, singletons are closed); and no converse implicatio...

Topological relations are one of the most fundamental properties between spatial objects. The topological relations between crisp spatial objects have been well identified. However how to formalise the topological relations between fuzzy regions needs more investigation. The paper starts from introduction of boundaries defined in the fuzzy topological space. By use of a definition formally equi...