# Homotopy-minimal manifold

From Topospaces

*This article defines a property of manifolds and hence also of topological spaces*

*This term is nonstandard and is being used locally within the wiki. For its use outside the wiki, please define the term when using it.*

## Contents

## Definition

### Symbol-free definition

A manifold is termed **homotopy-minimal** (*as a manifold*) if it is not homotopy-equivalent to a manifold of smaller dimension.

## Relation with other properties

### Stronger properties

- Compact manifold:
*For full proof, refer: Compact implies homotopy-minimal*