# Nondegenerate space

From Topospaces

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties 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 topological space is said to be **nondegenerate** if every point in it is a nondegenerate point, viz the inclusion of any point is a cofibration.

## Relation with other properties

### Stronger properties

property | quick description | proof of implication | proof of strictness (reverse implication failure) | intermediate notions |
---|---|---|---|---|

Manifold | Manifold implies nondegenerate | |FULL LIST, MORE INFO | ||

CW-space | CW implies nondegenerate | |FULL LIST, MORE INFO | ||

Compactly nondegenerate space | |FULL LIST, MORE INFO |

### Weaker properties

- Topological space which has a nondegenerate point

## Metaproperties

### Retract-hereditariness

This property of topological spaces is hereditary on retracts, viz if a space has the property, so does any retract of it

View all retract-hereditary properties of topological spaces

Any retract of a nondegenerate space is again nondegenerate.