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→Properties: spell out that this provides a dense set of local maxima (as a sequence of papers in the Monthly in the mid-1980s repeatedly studied this topic and failed to note this simple example) |
→Properties: proper |
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|<math>f</math> has a proper '''[[maxima and minima|local maximum]]''' at each rational number, providing an example of a function with a dense set of proper local maxima.<ref>{{cite journal|title=Solution to Problem 1129|first=Paolo|last=Perfetti|department=Problem Department|journal=Pi Mu Epsilon Journal|volume=12|issue=5|date=Fall 2006|pages=301–319|jstor=24337958}} Perfetti supplies the negation of Thomae's function as an example with a dense set of proper local minima.</ref>
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See the proofs for continuity and discontinuity above for the construction of appropriate [[neighborhood (mathematics)|neighbourhoods]], {{nowrap|where <math>f</math> has}} maxima.
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