Locally path-connected space

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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)