Smallest homotopically trivial non-contractible spaces

TL;DR

This paper characterizes the smallest topological spaces that are homotopically trivial but not contractible, identifying the minimal examples of such spaces.

Contribution

It provides a classification of the minimal homotopically trivial non-contractible spaces based on their point count.

Findings

Identified the minimal number of points for such spaces.

Provided a complete characterization of these minimal spaces.

Enhanced understanding of the relationship between homotopy and contractibility.

Abstract

We characterize the homotopically trivial non-contractible topological spaces with the minimum number of points.