Limiting Sets in Digital Topology

TL;DR

This paper introduces the concept of limiting sets in digital topology, generalizing existing notions like freezing and cold sets, and explores their properties to advance the understanding of fixed points in digital spaces.

Contribution

It proposes the new concept of limiting sets in digital topology, extending the theory of fixed points beyond previous notions.

Findings

Limiting sets generalize freezing and cold sets.

Properties of limiting sets are characterized.

Potential applications in digital fixed point theory.

Abstract

Freezing sets and cold sets have been introduced as part of the theory of fixed points in digital topology. In this paper, we introduce a generalization of these notions, the limiting set, and examine properties of limiting sets.