A Space is connected if any two points in can be connected by a curve lying wholly within . A Space is 0-connected (a.k.a. Pathwise-Connected) if every Map from a 0-Sphere to the Space extends continuously to the 1-Disk. Since the 0-Sphere is the two endpoints of an interval (1-Disk), every two points have a path between them. A space is 1-connected (a.k.a. Simply Connected) if it is 0-connected and if every Map from the 1-Sphere to it extends continuously to a Map from the 2-Disk. In other words, every loop in the Space is contractible. A Space is -Multiply Connected if it is -connected and if every Map from the -Sphere into it extends continuously over the -Disk.

A theorem of Whitehead says that a Space is infinitely connected Iff it is contractible.

© 1996-9

1999-05-26