Some Studies on Proximity Spaces

Abstract

Proximity spaces characterize the proximity relation, a relation that provides a framework for identifying the nearness of a point to a set and the nearness of two sets, where nearness is based on the spatial relationship between objects. In 1952, The concept of proximity spaces was initiated by Efremovi c [14]. Also, Lodato, and others [51, 52, 53, 62, 64] presented weaker axioms than those of Efremovi c. In proximity spaces, a compatible proximity can be introduced only in completely regular topological spaces but in generalized proximities can in fact be introduced in any topological spaces. proximity relation is applied to solving problems based on human perception [65] that arise in areas such as digital images [66]. There are several published researches on proximity spaces some of them exist in [62]. Steiner [74] introduced the notion of S-quasi proximity. Hayashi [25] studied bitopological space generated by S-quasi proximity. Recently, Kandil et. al. [40, 41, 44] introduced a new approaches of proximity structure based on the