Theorem
125
[0VV]Suppose \((X,d)\) is complete.
Given countably many sets \(A_ n\) that are open and dense in \(X\), we have that \(β_ n A_ n\) is dense.
Given countably many sets \(C_ n\) closed with empty interior in \(X\), we have that \(β_ n C_ n\) has empty interior.