thin set

A subset E of a topological space S is said to be of first category in S if E can be written as the countable union of subsets which are nowhere dense in S, i.e., if E is expressible as a union E = union _(n element N) E_n where each subset E_n subset S is nowhere dense in S. Informally, one thinks of a first category subset as a "small" subset of the host space and indeed, sets of first category are sometimes referred to as meager. Sets which are not of first category are of second category.