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  "body": "\n## Definition\n\nLet $(X, d)$ be a [[metric space|063W5JMY85]] and let $A$ be a [[subset|0FE8Q5S42Y]] of $X$.\nThe subspace metric on $A$ is the function $d_A \\colon A \\times A \\to \\mathbb{R}$ with $d_A(a, b) = d(a, b)$ for all $a, b \\in A$.\nIt is the [[restriction|0D2MXBV21T]] of $d$ to $A \\times A$.\nThe metric space $(A, d_A)$ is a subspace of $(X, d)$.\n\n## Remarks\n\nThe function $d_A$ is a metric, because each axiom for $d_A$ is a special case of the same axiom for $d$.\nFor example, the interval $[0, 1]$ with $d(x, y) = |x - y|$ is a subspace of the [[real line|0KXJTZSW9B]].\nThe open sets of $(A, d_A)$ are the sets $U \\cap A$ with $U$ open in $X$. Thus the topology of $d_A$ is the [[subspace topology|0D5YHQGDJY]].\n\n## Explanations\n\n### L1 human\n\nA subspace keeps the distances of the big space and forgets the other points.\nFor example, the unit circle in the plane, with the Euclidean distance, is a subspace of $\\mathbb{R}^2$. The distance between two points of the circle is the length of the straight chord, not of the arc.\n",
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