# 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 Generic 2013-03-22 13:40:30 2013-03-22 13:40:30 Koro (127) Koro (127) 10 Koro (127) Definition msc 54E52 generically