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[parent] 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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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:
AMS MSC54E52 (General topology :: Spaces with richer structures :: Baire category, Baire spaces)

Pending Errata and Addenda
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