Nondegenerate space

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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.


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



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.