Locally path-connected space: Difference between revisions
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A [[topological space]] is termed '''locally path-connected''' if given any point in it, and any open subset containing the point, there is a smaller open set containing the point, which is [[path-connected space|path-connected]] in the [[subspace topology]]. | A [[topological space]] is termed '''locally path-connected''' if given any point in it, and any open subset containing the point, there is a smaller open set containing the point, which is [[path-connected space|path-connected]] in the [[subspace topology]]. | ||
==Relation with other properties== | ==Relation with other properties== | ||
Latest revision as of 20:01, 30 May 2016
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 connectedness. View other variations of connectedness
Definition
A topological space is termed locally path-connected if given any point in it, and any open subset containing the point, there is a smaller open set containing the point, which is path-connected in the subspace topology.
Relation with other properties
Stronger properties
References
Textbook references
- Topology (2nd edition) by James R. MunkresMore info, Page 161 (formal definition, along with locally connected space)