6. Notions of countability

Theorem (Sierpiński, 1920). Every infinitely countable metric space with no isolated points is homeomorphic to $ℚ$ with its usual topology (p. 328 of ).

6.1 Countable bases of neighborhoods

A metric space has countable bases of neighborhoods (p. 102 of

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Notions of countability

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Bibliography

(1) - AARTS (J.M.), NISHIURA (T.) - Dimension and Extensions, - North Holland, 331 pages (1993).
(2) - ADAMS (C.), FRANZOSA (R.) - Introduction to Topology Pure and Applied, - Pearson, 507 pages (2008).
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