Image transformations on locally compact spaces

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.

arXiv commentKeywords: Banach algebras of continuous functions, Integration with respect to measures and other set functions, Set functions and measures on topological spaces, States, Logical foundations of quantum mechanics