A new topological perspective of expanding space-times with applications to cosmology

TL;DR

This paper explores a novel topological approach to understanding expanding space-times in cosmology, using the Tietze extension theorem to model cosmic expansion and its potential applications in mathematical physics.

Contribution

It introduces a topological framework for cosmic expansion based on the Tietze extension theorem, providing a new perspective in cosmological modeling.

Findings

Topological analogy between circle extension and cosmic expansion

Proposed a topological analogy to the cosmic scale factor

Suggested applications of topological extension in mathematical physics

Abstract

We discuss the possible role of the Tietze extension theorem in providing a rigorous topological base to the expanding space-time in cosmology. A simple toy model has been introduced to show the analogy between the topological extension from a circle $S$ to the whole space $M$ and the cosmic expansion from a non-zero volume to the whole space-time in non-singular cosmological models. A topological analogy to the cosmic scale factor function has been suggested, the paper refers to the possible applications of the topological extension in mathematical physics.