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  "body": "\n## Definition\n\nA topological space $X$ is *contractible* if the map from $X$ to a one-point space is a [[homotopy equivalence|XZG6MTSWCN]].\n\n## Remarks\n\nEquivalently, $X$ is nonempty and the identity map $\\id_X$ is [[null-homotopic|SMEV5BSQ5S]].\nA homotopy from $\\id_X$ to a constant map is called a *contraction* of $X$.\nThe empty space is not contractible, since there is no map from a point to it.\nExample: a convex subset $C \\neq \\emptyset$ of $\\R^n$ is contractible; for a fixed $c \\in C$, the map $H(x, t) = (1 - t) x + t c$ stays in $C$ by convexity and contracts $C$ to $c$.\nNon-example: the circle $S^1$ is not contractible, since its [[fundamental group|S1XK3HXHFX]] is $\\Z$, not trivial.\nEvery contractible space is [[path-connected|0WB6DH499T]].\n",
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