Compactly generated space
From Topospaces
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
Contents
Definition
Symbol-free 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.
Definition with symbols
A topological space is said to be compactly generated if there exists a collection of compact subsets of , such that a subset is open if and only if is open in for every .
Relation with other properties
Stronger properties
Metaproperties
References
Textbook references
- Topology (2nd edition) by James R. Munkres^{More info}, Page 283 (formal definition)