# Fixed Point Sets in Digital Topology, 2

## TL;DR

This paper advances digital topology by exploring fixed point invariants, introducing pointed versions, and defining freezing and cold sets to understand how fixed points influence continuous self-maps.

## Contribution

It introduces pointed fixed point invariants, freezing sets, and cold sets, extending previous work to better understand fixed point properties in digital images.

## Key findings

- Fixed point sets restrict the behavior of continuous maps.
- Introduction of freezing and cold sets to analyze fixed point influence.
- Extension of invariants to pointed versions in digital topology.

## Abstract

We continue the work of [10], studying properties of digital images determined by fixed point invariants. We introduce pointed versions of invariants that were introduced in [10]. We introduce freezing sets and cold sets to show how the existence of a fixed point set for a continuous self-map restricts the map on the complement of the fixed point set.