Contractible_Spaces, Homotopy Equivalence and Homeomorphism in Digital Topology

TL;DR

This paper explores contractible digital spaces, introduces new types of contractible digital spaces and transformations, and demonstrates how these can be used to relate digital manifolds through homotopy and homeomorphism.

Contribution

It introduces new contractible digital spaces and transformations, expanding the tools for digital topology analysis and manifold equivalence.

Findings

Defined new types of contractible digital spaces like cone and double cone

Developed six types of contractible transformations

Showed transformations can convert digital manifolds into homeomorphic counterparts

Abstract

This article provides a brief overview of the main results in the field of contractible digital spaces and contractible transformations of digital spaces and contains new results. We introduce new types of contractible digital spaces such as the cone and the double cone. Based on this, we introduce new contractible transformations that covert the digital space into a homotopy equivalent to the first one. We group together these transformations and get 6 types of contractible transformations. These transformations can be used to convert a closed digital n-dimensional manifold into another closed n-dimensional manifold homeomorphic to the first one.