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
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Cite this as:
Barile, Margherita. "Separable Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SeparableSpace.html