# Definition:Separable Space

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## Definition

A topological space $T = \struct {S, \tau}$ is **separable** if and only if there exists a countable subset of $S$ which is everywhere dense in $T$.

## Also see

- Results about
**separable spaces**can be found here.

## Sources

- 1970: Lynn Arthur Steen and J. Arthur Seebach, Jr.:
*Counterexamples in Topology*... (previous) ... (next): $\text{I}: \ \S 1$: Countability Properties - 1970: Lynn Arthur Steen and J. Arthur Seebach, Jr.:
*Counterexamples in Topology*... (previous) ... (next): $\text{I}: \ \S 3$: Countability Axioms and Separability