A set in R^n which can be reduced to one of its points, say P, by a continuous deformation, is said to be contractible. The transformation is such that each point of the set is driven to P through a path with the properties that 1. Each path runs entirely inside the set. 2. Nearby points move on "neighboring" paths. Condition (1) implies that a disconnected set, i.e., a set consisting of separate parts, cannot be contractible.
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