Let \(X\) be a topological space and let \(A\subseteq X\).
\(A\) is of first category in \(X\) if it is a countable union of nowhere dense subsets of \(X\).
\(A\) is of second category in \(X\) if it is not of first category in \(X\).
What does it mean for a subset to be of first category, and of second category?