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metric space

 Definition/Summary A metric space (A, d) is a set A paired with a function $d: A \times A \to \mathbb{R}$, such that for any elements x, y, z in A: \begin{align*} d(x,y) & \geq 0 \\ d(x,y) & = 0 \text{ if and only if } x = y \\ d(x,y) & = d(y,x) \\ d(x,z) & \leq d(x,y) + d(y,z) \end{align*} The function d is referred to as a metric or distance function.

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 Breakdown Mathematics > Calculus/Analysis >> General Analysis