For simplicity, we adopt the following rules: X, Y denote sets, n, m, k, i denote natural numbers, r denotes a real number, R denotes an element of RF, K denotes a field, f , f1, f2, g1, g2 denote finite sequences, r1, r2, r3 denote real-valued finite sequences, c1, c2 denote complex-valued finite sequences, and F denotes a function. Let us consider X, Y and let F be a positive yielding partial...

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...

in this paper we introduce entire sequence spaces defined by a sequence of modulus functions . we study some topological properties of these spaces and prove some inclusion relations.

The classical theorems of Riesz [l] on compact operators have been extended by Leray [2] and Williamson [3] to the context of topological linear spaces. Ringrose [4] has shown that if an operator on such a space is compact, the square of its adjoint is also compact, where the topology on the dual space is that of uniform convergence on bounded sets. Thus if an operator is continuous and some po...

A. Csaszar introduced and extensively studied the notion of generalized open sets. Following Csazar, we introduce a new notion hyperconnected. We study some specic properties about connected and hyperconnected in generalized topological spaces. Finally, we characterize the connected component in generalized topological spaces.

In this paper, we use the left(right) stabilizers of a BCKalgebra (X, &lowast, 0) and produce two basis for two different topologies. Then we show that the generated topological spaces by these basis are Bair, connected, locally connected and separable. Also we study the other properties of these topological spaces.