Compactly generated space: Difference between revisions
| Line 13: | Line 13: | ||
* [[Compact space]] | * [[Compact space]] | ||
* [[Locally compact space]] | * [[Locally compact space]] | ||
* [[First-countable space]] | * [[First-countable space]]: {{proofat|[[First-countable implies compactly generated]]}} | ||
* [[Metrizable space]] | * [[Metrizable space]] | ||
* [[CW-space]] | * [[CW-space]] | ||
==Metaproperties== | ==Metaproperties== | ||
Revision as of 01:17, 2 February 2008
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 is a variation of compactness. View other variations of compactness
Definition
A topological space is said to be compactly generated if the topology on it is generated by a collection of compact subsets. In other words, a set in the topological space is open if and only if its intersection with each of the compact subsets is open, in the subspace topology.
Relation with other properties
Stronger properties
- Compact space
- Locally compact space
- First-countable space: For full proof, refer: First-countable implies compactly generated
- Metrizable space
- CW-space