Semi Compactness Space in Bornological Space

Abstract

The idea of bounded subset of a topological vector space was introduced by von Neumann. As a result of playing an important role in functional analysis that motivated the concept of more general and abstract classes of bounded sets, it is called bornology. That means, it is applied to solve the questions of boundedness for any space or set in general way not only by usual definition of bounded set. However, we take a collection of subset of , such that, satisfying three conditions,cover , and stable under hereditary, i.e., if then also finite union. Basically, a bornological space is a type of spaces which possesses the minimum amount of the structure needed to address the question of boundedness of sets and functions. In addition, since bornology has shown to be a very useful tool in various aspects of functional analysis, it has been considered by several researchers in different areas. In this paper, we consider the concept of semi-compactness in bornological space and study some of its properties.