Strongly near proximity \& hyperspace topology

TL;DR

This paper introduces a new type of proximity called strongly near proximity and develops a hit-and-miss topology on the hyperspace of closed sets based on this proximity, advancing topological concepts.

Contribution

It presents the concept of strongly near proximity and constructs a corresponding hit-and-miss topology on the hyperspace of nonempty closed subsets.

Findings

Introduction of strongly near proximity as a new proximity concept

Development of a hit-and-miss topology based on this proximity

Establishment of topological properties of the hyperspace

Abstract

This article introduces strongly near proximity, which represents a new kind of proximity called \emph{almost proximity}. A main result in this paper is the introduction of a hit-and-miss topology on ${CL}(X)$, the hyperspace of nonempty closed subsets of $X$, based on the strongly near proximity.