Topological property
Summary
A topological property is a property of topological spaces such that, if a space has it, each homeomorphic space also has it. Examples are compactness, connectedness, separability, metrizability and the Hausdorff property.
Remarks
Topological properties are used to show that two spaces are not homeomorphic. For example, is compact and is not, so they are not homeomorphic. Properties that depend on a metric are often not topological. For example, and are homeomorphic, but only is complete and only is bounded.
Further reading
- Web https://en.wikipedia.org/wiki/Topological_property, lead section
- Web https://en.wikipedia.org/wiki/Topological_property, Non-topological properties
About this page
| Tag | 02SMVGC690 |
|---|---|
| URI | m2://02SMVGC690 |
| Aliases | topological-invariant |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54A05 |
| Same as |
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What this page needs for W2
- edge defines in: at least one definition (0 of 1)
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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