First category means a countable union of nowhere dense sets; second category means not first category.Suggest a slogan
Let \(X\) be a topological space and \(A\subseteq X\). Then \(A\) is of first category in \(X\) if and only if \(A\) is a countable union of nowhere dense subsets of \(X\), and of second category in \(X\) otherwise.
What is a first category set? A second category?