Nondegenerate space
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
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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.