# equivalent statement of Baire category 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.

Title equivalent statement of Baire category theorem EquivalentStatementOfBaireCategoryTheorem 2013-03-22 14:04:49 2013-03-22 14:04:49 gumau (3545) gumau (3545) 8 gumau (3545) Theorem msc 54E52