A topological space having a countable dense subset. An example is the Euclidean space with the Euclidean topology, since it has the rational lattice as a countable dense subset and it is easy to show that every open -ball contains a point whose coordinates are all rational.
See alsoHilbert Cube, Urysohn's Metrization Theorem
This entry contributed by Margherita Barile
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Barile, Margherita. "Separable Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SeparableSpace.html