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|Noun||1.||metric space - 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|
mathematical space, topological space - (mathematics) any set of points that satisfy a set of postulates of some kind; "assume that the topological space is finite dimensional"
Euclidean space - a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
Hilbert space - a metric space that is linear and complete and (usually) infinite-dimensional