# Space in which every retraction is a deformation retraction

From Topospaces

## Contents

## Definition

A **space in which every retraction is a deformation retraction** is a topological space with the property that any retraction math>r:X \to Y</math> for a subspace of (with the subspace topology) arises as a deformation retraction, i.e., there is a homotopy from the identity map to that retraction that restricts to on the subspace at all time.

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

topologically convex space | Template:Intermediate notions |

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

contractible space | |FULL LIST, MORE INFO | |||

SDR-contractible space | |FULL LIST, MORE INFO |