generic

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 $x\in X$. The useful fact about generic properties is that, given countably many generic properties $P_n$, all of them hold simultaneously in a residual set, i.e. we have that, generically, $P_n(x)$ 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