# Locally simply connected space

From Topospaces

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

## Contents

## Definition

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

- For every point , and every open subset of containing , there is an open subset of contained in , and which is simply connected in the subspace topology from .
- has a basis of open subsets each of which is a simply connected space with the subspace topology.