Variable Topology on Fractal Manifold

TL;DR

This paper explores a variable topology framework on fractal manifolds, linking universe expansion to topological variation, offering a novel mathematical model for cosmological dynamics.

Contribution

It introduces a family of topologies on fractal manifolds and connects topological changes to universe expansion, providing a new perspective in cosmological modeling.

Findings

Fractal manifold topology is a family of variable topologies.

Universe expansion correlates with topology variation.

Provides a new mathematical framework for cosmology.

Abstract

In this paper, we study the topology associated to the fractal manifold model. It turns out that this topology is actually a family of topologies that gives to the fractal manifold a structure of variable topological space. Additionally, we prove that using the fractal manifold as model for the universe dynamic, the universe expansion is intimately correlated to the variation of the topology.