Singularities in Space-time Foam Algebras

TL;DR

This paper investigates the structure of singularity sets in space-time foam algebras of generalized functions, showing an isomorphism with closed nowhere dense algebras and discussing the handling of singularities.

Contribution

It demonstrates the isomorphism between a specific space-time foam algebra and closed nowhere dense algebras, expanding understanding of singularities in these frameworks.

Findings

The algebra defined with an asymptotic vanishing condition is isomorphic to closed nowhere dense algebras.

The paper discusses the types of singularities manageable within space-time foam algebras.

Abstract

In this paper we consider the structure of the singularity sets associated with generalized functions in certain space-time foam algebras of generalized functions. In particular, we consider the algebra that is defined in terms of an asymptotic vanishing condition outside sets of first Baire category. It is shown that this algebra is in fact isomorphic to the earlier closed nowhere dense algebras. We also discuss general questions regarding singularities that can be handled in space-time foam algebras.