A topological space X is contractible iff it is homotopic to a point.

That is, there exists a continuous f:X×[0,1] → X such that ∀x∈X f(x,0)=x and f(x,1)=a (for some fixed point a).

In particular, X is path connected; moreover, it must also be simply connected.

Any convex set (and every star convex set) in Rn is contractible.

Con*tract"i*ble (?), a.

Capable of contraction.

Small air bladders distable and contractible. Arbuthnot.

 

© Webster 1913.

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