# Suspension of contractible space is contractible

From Topospaces

This article gives the statement, and possibly proof, of a topological space property (i.e., contractible space) satisfying a topological space metaproperty (i.e., suspension-closed property of topological spaces)

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## Statement

Suppose is a contractible space. Then, the Suspension (?) of , denoted , is also a contractible space.

## Related facts

- Suspension of any space is path-connected
- Suspension of path-connected space is simply connected, which uses the Seifert-van Kampen theorem
- Homology for suspension, which uses the Mayer-Vietoris homology sequence
- Suspension pushes up connectivity by one
- Suspension of weakly contractible space is weakly contractible