A separable space is a topological space having a countable dense set.
An example is the Euclidean space 
with the Euclidean topology,
since it has 
as a countable dense set
and every open ball contains a point
whose coordinates are all rational.
Separable Space
See also
Dense Set, Hilbert Cube, Lipschitz Isomorphism Problem, Separable Quotient Problem, Urysohn's Metrization TheoremThis entry contributed by Margherita Barile
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Cite this as:
Weisstein, Eric W., with contributions by Margherita Barile. "Separable Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SeparableSpace.html