Locally path-connected space
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.
Formalisms
In terms of the strongly locally operator
This property is obtained by applying the strongly locally operator to the property: path-connected space
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)