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| A '''metric space''' is a [[Analysis/Sets|set]] for which a distance function can be defined. | A '''metric space''' is a [[Analysis/Sets|set]] for which a distance [[Analysis/Functions|function]] can be defined. |
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| A metric space is a [[Analysis/Sets|set]] with a distance (or metric) function as ''d: M × M -> R''. | A metric space is a [[Analysis/Sets|set]] with a distance (or metric) [[Analysis/Functions|function]] as ''d: M × M -> R''. |
Metric Space
A metric space is a set for which a distance function can be defined.
Not to be confused with a measure space.
Contents
Description
A metric space is a set with a distance (or metric) function as d: M × M -> R.
For any p and q in M, the distance must feature these properties:
d(p,q) ≥ 0, and d(p,q) = 0 only if p = q
Symmetry: d(p,q) = d(q,p)