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  "body": "\n## Definition\n\nLet $m \\ge 1$ be an integer, and let $S^1 \\sqcup \\cdots \\sqcup S^1$ be the disjoint union of $m$ copies of the [[circle|060W5CBZP6]].\n\n1. A *link with $m$ components* is a subset $L \\subset \\R^3$ of [[Euclidean space|0XPR1E85W0]] that is the image of a continuous injective map from $S^1 \\sqcup \\cdots \\sqcup S^1$ to $\\R^3$.\n2. The *components* of $L$ are the images of the $m$ circles.\n3. Two links $L$ and $L'$ are *equivalent* if there is a continuous family of [[homeomorphisms|0QT00PB5G2]] $h_t \\colon \\R^3 \\to \\R^3$, $t \\in [0, 1]$, with $h_0 = \\id$ and $h_1(L) = L'$.\n\n## Remarks\n\nA link with one component is a knot.\nAs for knots, one usually restricts to tame links, those equivalent to a union of closed polygons.\nExample: two disjoint round circles in the plane $z = 0$, far apart, form a link with $2$ components, the *unlink* of two components.\nNon-example: two circles that meet in one point do not form a link, because the map from the disjoint union is not injective.\nLinks are often oriented, by choosing a direction on each component.\n",
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