AConsequenceOfBaireCategoryTheorem 2003-12-01 23:45:37 2003-12-16 15:29:57 Theorem Baire category theorem % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here Let $(X,d)$ be a complete metric space. Then every subset $B\subset X$ of first category has empty interior. \newline \newline \textbf{Corollary}: Every non empty complete metric space is of second category.