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 Theorem
*This 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