In general every continuous function can have this property but for polynomial it's true then what is that unique property that a polynomial have but not true for a general continuous function??
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Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community May 24 '23 at 11:02
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If $f$ is a non-constant polynomial then $|f(x)| \to \infty$ as $x \to \pm \infty$. Use sequential definition of closed sets. – geetha290krm May 24 '23 at 11:21
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If a continuous function between locally compact Hausdorff spaces is proper then it is also closed. – Anne Bauval May 24 '23 at 11:47
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I'm not sure I get your question. You literally just said what is the property that polynomials have but general continuous functions don't have to have... Also, what do you mean by "unique"? Very confusing question. – freakish May 24 '23 at 12:24