TOPICS
Search

Separable Space


A topological space having a countable dense subset. An example is the Euclidean space R^n with the Euclidean topology, since it has the rational lattice Q^n as a countable dense subset and it is easy to show that every open n-ball contains a point whose coordinates are all rational.


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

Subject classifications