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 locally operator

This property is obtained by applying the locally operator to the property: path-connected space

Relation with other properties

Stronger properties

• Locally simply connected space
• Locally contractible space

References

Textbook references

• Topology (2nd edition) by James R. Munkres^{More info}, Page 161 (formal definition, along with locally connected space)