Multiply Connected

A set which is connected but not simply connected is called multiply connected. A space is n-multiply connected if it is (n-1)-connected and if every map from the n-sphere into it extends continuously over the (n+1)-disk

A theorem of Whitehead says that a space is infinitely connected iff it is contractible.

See also

Connected Space, Locally Pathwise-Connected, Pathwise-Connected, Simply Connected

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Cite this as:

Weisstein, Eric W. "Multiply Connected." From MathWorld--A Wolfram Web Resource.

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