Loop space: Difference between revisions
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Loop space may refer to either of these: | Loop space may refer to either of these: | ||
* [[Loop space of a topological space]], which is the space of all [[continuous map]]s from the [[ | * [[Loop space of a topological space]], which is the space of all [[continuous map]]s from the [[circle]] to the topological space under the [[compact-open topology]]. | ||
* [[Loop space of a based topological space]], which is the space of all basepoint-preserving continuous maps from the | * [[Loop space of a based topological space]], which is the space of all basepoint-preserving continuous maps from the circle to the topological space, again with the compact-open topology. | ||
Latest revision as of 02:34, 9 November 2010
Loop space may refer to either of these:
- Loop space of a topological space, which is the space of all continuous maps from the circle to the topological space under the compact-open topology.
- Loop space of a based topological space, which is the space of all basepoint-preserving continuous maps from the circle to the topological space, again with the compact-open topology.