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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 $n$ .
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"generic" is owned by Koro.
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| Also defines: |
generically |
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Cross-references: proposition, Baire space, subset, residual, property
There are 12 references to this entry.
This is version 7 of generic, born on 2003-06-11, modified 2003-07-25.
Object id is 4341, canonical name is Generic.
Accessed 4639 times total.
Classification:
| AMS MSC: | 54E52 (General topology :: Spaces with richer structures :: Baire category, Baire spaces) |
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Pending Errata and Addenda
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