# Image transformations on locally compact spaces

## TL;DR

This paper extends the theory of image transformations, which are structure-preserving maps, from compact to locally compact Hausdorff spaces, broadening the mathematical framework for analyzing images in topological spaces.

## Contribution

It generalizes existing results on algebraic image transformations from compact to locally compact spaces, enhancing the theoretical foundation in topology and measure theory.

## Key findings

- Extended results of Aarnes to locally compact spaces
- Characterized algebra homomorphisms as image transformations
- Broadened the applicability of structure-preserving maps in topology

## Abstract

An image is here defined to be a set which is either open or closed and an image transformation is structure preserving in the following sense: It corresponds to an algebra homomorphism for each singly generated algebra. The results extend parts of results of J.F. Aarnes on quasi-measures, -states, -homomorphisms, and image-transformations from the setting compact Hausdorff spaces to locally compact Hausdorff spaces.