Simply connected space: Difference between revisions
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A [[topological space]] is said to be '''simply connected''' if it satisfies the following equivalent conditions: | A [[topological space]] is said to be '''simply connected''' if it satisfies the following equivalent conditions: | ||
* It is path-connected, and any loop at any point is homotopic to the constant loop at that point | * It is [[path-connected space|path-connected]], and any loop at any point is homotopic to the constant loop at that point | ||
* It is path-connected, and its [[fundamental group]] is trivial | * It is path-connected, and its [[fundamental group]] is trivial | ||
Revision as of 23:22, 2 November 2007
This article defines a homotopy-invariant property of topological spaces, i.e. a property of homotopy classes of topological spaces
View other homotopy-invariant properties of topological spaces OR view all properties of topological spaces
Definition
Symbol-free definition
A topological space is said to be simply connected if it satisfies the following equivalent conditions:
- It is path-connected, and any loop at any point is homotopic to the constant loop at that point
- It is path-connected, and its fundamental group is trivial
Definition with symbols
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