A topological space \(X\) is a Baire space if whenever \((U_n)_{n\geq 1}\) is a countable family of open dense subsets of \(X\), the intersection \(\bigcap_{n\geq 1} U_n\) is dense in \(X\).
What does it mean for $X$ to be a Baire space?
Baire space
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