Metric (analysis)
A metric on a set is a function which obeys the following three properties:
- Symmetry: for all points .
- Positivity: for all and if and only if .
- The triangle inequality: for all .
Together, the set and the metric form a metric space.
Every metric space can be used to form a topology by considering taking the set of open balls as a topological basis (i.e. the sets ).
Common metrics
- For , the Euclidean metric is the conventional distance function.
- For any set , the discrete metric and otherwise.
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