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Exists one submersion F:R^{3}-{0}------>R such that, there are c1 and c2 in R such that f^{-1}(c1) is compact and f^{-1}(c2) is noncampact.

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 Yes, such functions exist, for all $n \geq 2$ $f:\mathbb R^n \setminus \{0\} \to \mathbb R$. They should be expressible as some rational function in trig functions. But I think math.stackexchange.com is a more appropriate forum for your question. – Ryan Budney Jul 23 2011 at 6:36

closed as too localized by Ryan Budney, Andres Caicedo, Andreas Thom, Andreas Blass, José Figueroa-O'Farrill Jul 23 2011 at 12:32

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