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
Canonical name	EquivalentStatementOfBaireCategoryTheorem
Date of creation	2013-03-22 14:04:49
Last modified on	2013-03-22 14:04:49
Owner	gumau (3545)
Last modified by	gumau (3545)
Numerical id	8
Author	gumau (3545)
Entry type	Theorem
Classification	msc 54E52