A property that holds for all x in some residualPlanetmathPlanetmathPlanetmath subset of a Baire spacePlanetmathPlanetmath X is said to be genericPlanetmathPlanetmathPlanetmath 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 propositionPlanetmathPlanetmath about xX. 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.

Title generic
Canonical name Generic
Date of creation 2013-03-22 13:40:30
Last modified on 2013-03-22 13:40:30
Owner Koro (127)
Last modified by Koro (127)
Numerical id 10
Author Koro (127)
Entry type Definition
Classification msc 54E52
Defines generically