Locally simply 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

Definition

Symbol-free definition

A topological space is said to be locally simply connected if given any point and any open subset containing that point, there exists a smaller open set containing the point, which is simply connected in the subspace topology.

Relation with other properties

Stronger properties

• Locally contractible space

Weaker properties

• Semilocally simply connected space
• Locally path-connected space
• Connected space