Noun
a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality
Source: WordNetAn important consequence is that every metric space admits partitions of unity and that every continuous real-valued function defined on a closed subset of a metric space can be extended to a continuous map on the whole space ( Tietze extension theorem ). Source: Internet
Analysis may be distinguished from geometry ; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space ) or specific distances between objects (a metric space ). Source: Internet
Also: if a non-empty complete metric space is the countable union of closed sets, then one of these closed sets has non-empty interior. Source: Internet
A rather different type of example is afforded by a metric space X which has the discrete metric (where any two distinct points are at distance 1 from each other). Source: Internet
Also every subspace of a separable metric space is separable. Source: Internet
As a Euclidean space is a metric space, the conditions in the next subsection also apply to all of its subsets. Source: Internet