Open sets of conservative matrices

Open Sets of Conservative Matrices1

In this paper we present two principal results. In Theorem 1 we show that if r¡ denotes the open set of (conservative) matrices which map some subspace of c of infinite deficiency isomorphically onto c and if A denotes the closed set of matrices which sum some bounded divergent sequence, then [r']~=A. In Theorem 2 we produce a class of triangular matrices with the property that no triangular ma...

Applications of fuzzy $e$-open sets

The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated via fuzzy $e$-open sets.

Some results on maximal open sets

In this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. Some results about existence of maximal m-open setsare given. Moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.Our results are supported by examples and counterexamples.

On Pre-θ-Open Sets and Two Classes of Functions

Some points on generalized open sets

The paper is an attempt to represent a study of limit points, boundary points, exterior points, border, interior points and closure points in the common generalized topological space. This paper takes a look at the possibilities of an extended topological space and it also considers the new characterizations of dense set.