= Fréchet embedding
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Fix a point $x_0$ in a <metric space> $X$. The Fréchet embedding sends $x$ to the bounded function $a\mapsto d(x,a)-d(x_0,a)$ in $\ell^\infty(X)$. The <triangle inequality> bounds each coordinate by $d(x,x_0)$ and gives $\|f_x-f_y\|_\infty\leq d(x,y)$. Taking $a=x$ gives equality, so the map is an <isometric embedding>. For a separable metric space a countable dense set of anchors suffices. Finite collections of distances to selected subsets instead give one-Lipschitz coordinates that need not be an exact Fréchet embedding.
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