Uniformly based 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
A topological space is said to be uniformly based if it has a basis of open sets, for which all basis elements are homeomorphic. The abstract space to which they are all homeomorphic is termed the basis space.
Relation with other properties
Stronger properties
- Manifold: The basis space here is Euclidean space
Facts
For any property of topological spaces, a uniformly based space satisfies the property locally if and only if its basis space satisfies the property locally .