# Cofibration

From Topospaces

*This article defines a property over pairs of a topological space and a subspace, or equivalently, properties over subspace embeddings (viz, subsets) in topological spaces*

## Contents

## Definition

A subspace of a topological space is said to be a **cofibration**, or to have the **homotopy extension property** if the following holds: given any map and a homotopy such that , we have a homotopy whose restriction to is , and such that .

## Relation with other properties

### Stronger properties

### Weaker properties

- Closed subset in a Hausdorff space:
*For full proof, refer: Cofibration implies closed subset in Hausdorff space*

## Metaproperties

### Transitivity

*This property of subspaces of topological spaces is transitive. In other words, if satisfies the property as a subspace of and satisfies the property as a subspace of then satisfies the property as a subspace of *