meager set | 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 thin sets or meager set. Sets which are not of first category are of second category. An important distinction should be made between the above-used notion of "category" and category theory. Indeed, the notions of first and second category sets are independent of category theory.