Homogeneous 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
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 |