A **metric space** is an ordered pair where is a set and is a metric on, i.e., a function

such that for any, the following holds:

- (
*non-negative*), - iff (
*identity of indiscernibles*), - (
*symmetry*) and - (
*triangle inequality*) .

The first condition follows from the other three, since:

The function is also called *distance function* or simply *distance*. Often, is omitted and one just writes for a metric space if it is clear from the context what metric is used.

Read more about Metric Space: Examples of Metric Spaces, Open and Closed Sets, Topology and Convergence, Types of Maps Between Metric Spaces, Notions of Metric Space Equivalence, Topological Properties, Distance Between Points and Sets; Hausdorff Distance and Gromov Metric, Product Metric Spaces, Quotient Metric Spaces, Generalizations of Metric Spaces

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