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.
Separable Space
See also
Hilbert Cube, Urysohn's Metrization TheoremThis entry contributed by Margherita Barile
Explore with Wolfram|Alpha
Cite this as:
Barile, Margherita. "Separable Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SeparableSpace.html