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equivalent statement of Baire category theorem

(Theorem)

Let $(X,d)$ be a complete metric space. Then every subset $B\subset X$ of first category has empty interior.

Corollary: Every non empty complete metric space is of second category.

"equivalent statement of Baire category theorem" is owned by gumau.

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Attachments:: proof for one equivalent statement of Baire category theorem (Proof) by gumau

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Cross-references: interior, first category, subset, metric space, complete

This is version 5 of equivalent statement of Baire category theorem, born on 2003-12-01, modified 2003-12-16.
Object id is 5441, canonical name is AConsequenceOfBaireCategoryTheorem.
Accessed 2759 times total.

Classification:

54E52 (General topology :: Spaces with richer structures :: Baire category, Baire spaces)

Pending Errata and Addenda

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