generic (original) (raw)

A property that holds for all x in some residual subset of a Baire space X is said to be generic in X, or to hold generically in X. In the study of generic properties, it is common to state “generically, P⁢(x)”, where P⁢(x) is some proposition about x∈X. The useful fact about generic properties is that, given countably many generic properties Pn, all of them hold simultaneously in a residual set, i.e. we have that, generically, Pn⁢(x) holds for each n.