A topological space that contains a homeomorphic image of every topological space of a certain class. A metric space U is said to be universal for a family of metric spaces ℳ if any space from ℳ is isometrically embeddable in U. Fréchet proved that ℓ^∞, the space of all bounded sequences of real numbers endowed with a supremum norm, is a universal space for the family ℳ of all separable metric spaces. Holsztynski proved that there exists a metric d on R, inducing the usual topology, such that every finite metric space embeds in (R, d).
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