The Proof of Baire's Category Theorem
Definition
A Baire Space is a dense space for every sequence of all dense open subsets $\displaystyle \bigcap_{n=1}^{\infty} O_{n}$ of a topological space $X$.
A Baire Space is a dense space for every sequence of all dense open subsets $\displaystyle \bigcap_{n=1}^{\infty} O_{n}$ of a topological space $X$.