Countability axioms

Second countability axiom

A topological space (𝑋,T) is called second-countable iff it has a countable Topological basis. #m/def/topology

Properties

• Sequential compactness and 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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