Baire Category Theorem/Corollary/Proof 2

Corollary to Baire Category Theorem

The real number line $\R$ with the usual (Euclidean) metric is non-meager.

Proof

This proof does not use the Axiom of Dependent Choice, as it uses intrinsic properties of the real numbers that do not necessarily hold for the general complete metric space.

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Source of Name

This entry was named for René-Louis Baire.

Sources

• 1973: Thomas J. Jech: The Axiom of Choice ... (previous) ... (next): $1.$ Introduction: $1.4$ Problems: $5$