Homogeneous space: Difference between revisions
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! property !! quick description !! proof of implication !! proof of strictness (reverse implication failure) !! intermediate notions | ! property !! quick description !! proof of implication !! proof of strictness (reverse implication failure) !! intermediate notions | ||
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| [[Weaker than::Underlying space of topological group]] || underlying space for a [[topological group]] || [[underlying space of topological group implies homogeneous]] || || | | [[Weaker than::Underlying space of topological group]] || underlying space for a [[topological group]] || [[underlying space of topological group implies homogeneous]] || || | ||
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| [[Weaker than::Underlying space of T0 topological group]] || underlying space for a [[T0 topological group]] || | | [[Weaker than::Underlying space of T0 topological group]] || underlying space for a [[T0 topological group]] || || || | ||
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| [[Weaker than::Connected manifold]] || || [[connected manifold implies homogeneous]] || || {{intermediate notions short|homogeneous space|connected manifold}} | | [[Weaker than::Connected manifold]] || || [[connected manifold implies homogeneous]] || || {{intermediate notions short|homogeneous space|connected manifold}} | ||
Revision as of 14:55, 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
Definition
Symbol-free definition
A topological space is said to be homogeneous if given any two points in it, there is a homeomorphism from the topological space to itself that maps the first point to the second.
Relation with other properties
Stronger properties
| property | quick description | proof of implication | proof of strictness (reverse implication failure) | intermediate notions |
|---|---|---|---|---|
| Underlying space of topological group | underlying space for a topological group | underlying space of topological group implies homogeneous | ||
| Underlying space of T0 topological group | underlying space for a T0 topological group | |||
| Connected manifold | connected manifold implies homogeneous | |FULL LIST, MORE INFO | ||
| Compactly homogeneous space |