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

© 1996-9 Eric W. Weisstein