Separable Space

A topological space having a countable dense subset. An example is the Euclidean space R^n with the Euclidean topology, since it has the rational lattice Q^n as a countable dense subset and it is easy to show that every open n-ball contains a point whose coordinates are all rational.

See also

Hilbert Cube, Urysohn's Metrization Theorem

This entry contributed by Margherita Barile

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Cite this as:

Barile, Margherita. "Separable Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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