This is a continuation of [6]. In this article, we proved that convex combination on convex family is convex. and [9] provide the notation and terminology for this paper. 1. CONVEX COMBINATIONS ON CONVEX FAMILY The following propositions are true: (1) For every non empty RLS structure V and for all convex subsets M, N of V holds M ∩ N is convex. (2) Let V be a real unitary space-like non empty ...

Introduction. Kakutani's fixed point theorem [3]1 states that in Euclidean «-space a closed point to (nonvoid) convex set map of a convex compact set into itself has a fixed point. Kakutani showed that this implied the minimax theorem for finite games. The object of this note is to point out that Kakutani's theorem may be extended to convex linear topological spaces, and implies the minimax the...

Let a topological space. An intersection graph on a topological space , which denoted by ‎ , is an undirected graph which whose vertices are open subsets of and two vertices are adjacent if the intersection of them are nonempty. In this paper, the relation between topological properties of  and graph properties of ‎  are investigated. Also some classifications and representations for the graph ...

The aim of this paper is to study the categorical relations between matroids, Goetschel-Voxman’s fuzzy matroids and Shi’s fuzzifying matroids. It is shown that the category of fuzzifying matroids is isomorphic to that of closed fuzzy matroids and the latter is concretely coreflective in the category of fuzzy matroids. The category of matroids can be embedded in that of fuzzifying matroids as a ...

In this paper, we introduce the Orlicz sequence spaces generated by Cesàro mean of order one associated with a fixed multiplier sequence of non-zero scalars. Furthermore, we emphasize several algebraic and topological properties relevant to these spaces. Finally, we determine the Köthe-Toeplitz dual of the spaces `M (C, Λ) and hM (C, Λ). 1. Preliminaries, Background and Notation By ω, we denote...

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.

In this paper we characterize various sorts of boundedness of the free (abelian) topological group F (X) (A(X)) as well as the free locally-convex linear topological space L(X) in terms of properties of a Tychonoff space X. These properties appear to be close to so-called selection principles, which permits us to show, that (it is consistent with ZFC that) the property of Hurewicz (Menger) is l...

This paper addresses Tikhonov like regularization methods with convex penalty functionals for solving nonlinear ill-posed operator equations formulated in Banach or, more general, topological spaces. We present an approach for proving convergence rates which combines advantages of approximate source conditions and variational inequalities. Precisely, our technique provides both a wide range of ...

in this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. we also investigate effect to fuzzy soft connectedness. moreover, c_i-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.