Locally simply 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

Definition

A topological space X is termed locally simply connected if it satisfies the following equivalent conditions:

  1. For every point x \in X, and every open subset V of X containing x, there is an open subset U of X contained in V, and which is simply connected in the subspace topology from X.
  2. X has a basis of open subsets each of which is a simply connected space with the subspace topology.

Relation with other properties

Stronger properties

Weaker properties