Proximity spaces via hereditary classes

Subject Areas : General topology

Gh. Mirhosseinkhani ¹

1 - Department of Mathematics and Computer Sciences, Sirjan University of Technology, Sirjan, Iran

Received: 2022-11-18 Accepted : 2022-12-16 Published : 2022-12-01

Keywords: Generalized topology, H-proximity space, Hereditary class,

Abstract :

‎A hereditary class on a set $X$ is a nonempty collection of subsets of $X$ which is closed under‎ ‎subsets‎. ‎In this paper‎, ‎we present a new structure of proximity spaces by using a hereditary class‎, ‎called‎ ‎$\mathcal{H}$-proximity spaces‎, ‎as a generalization of Efremovi$\check{c}$ proximity spaces‎, ‎$I$-proximity spaces and‎ ‎coarse proximity spaces‎. ‎Some properties of this proximity structure and generalized topology induced by it are studied‎.

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