[[Countability axioms]]
# Second countability axiom

A topological space $(X, \mathcal{T})$ is called **second-countable** iff it has a countable [[Topological basis]]. #m/def/topology

## Properties

- [[Sequentially compact space|Sequential compactness]] and [[Compact space|compactness]] are equivalent in a second-countable space.
- [[Second countable implies Lindelöf]]

## Examples

- [[Real coördinate space]] with the usual topology has a countable basis given by balls with rational centres and rational radii.

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