# 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 |