A subset E of a topological space S is said to be of second category in S if E cannot be written as the countable union of subsets which are nowhere dense in S, i.e., if writing E as a union E = union _(n element N) E_n implies that at least one subset E_n subset S fails to be nowhere dense in S. Said differently, any set which fails to be of first category is necessarily second category and unlike sets of first category, one thinks of a second category subset as a "non-small" subset of its host space. Sets of second category are sometimes referred to as nonmeager.

Baire category theorem | first category | meager set | nonmeager set | nowhere dense