Timeline for Real analytic map with connected fibers
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Aug 14, 2022 at 12:42 | comment | added | aglearner | Dear Jason, many thanks for this answer, it's great that it is so simple! | |
| Aug 12, 2022 at 0:28 | comment | added | Jason Starr | That follows from point-set topology. For every partition $X=X'\sqcup X''$ into disjoint open and closed subsets, the images $f(X')$ and $f(X'')$ are closed subsets (since $f$ is proper). Since all fibers are connected (hence nonempty), the two subsets $f(X')$ and $f(X'')$ are disjoint and cover $Y$. Since $Y$ is connected, precisely one of $f(X')$ or $f(X'')$ is empty, and thus also $X'$, resp. $X''$, is nonempty. | |
| Aug 11, 2022 at 23:35 | history | asked | aglearner | CC BY-SA 4.0 |