Nondegenerate space: Difference between revisions
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===Stronger properties=== | ===Stronger properties=== | ||
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! property !! quick description !! proof of implication !! proof of strictness (reverse implication failure) !! intermediate notions !! comparison | |||
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| [[Weaker than::Manifold]] || || [[Manifold implies nondegenerate]] || || {{intermediate notions|nondegenerate space|manifold}} | |||
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| [[Weaker than::CW-space]] || || [[CW implies nondegenerate]] || || {{intermediate notions|nondegenerate space|CW-space}} | |||
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| [[Weaker than::Compactly nondegenerate space]] || || || || {{intermediate notions|nondegenerate space|compactly nondegenerate space}} | |||
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===Weaker properties=== | ===Weaker properties=== | ||
Revision as of 19:23, 24 October 2009
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.
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 | comparison |
|---|---|---|---|---|---|
| Manifold | Manifold implies nondegenerate | Template:Intermediate notions | |||
| CW-space | CW implies nondegenerate | Template:Intermediate notions | |||
| Compactly nondegenerate space | Template:Intermediate notions |
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.