Thomae's function: Difference between revisions

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Line 84: {{Collapse bottom}} \|<math>f</math> has a ~~strict~~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> {{pb}} See the proofs for continuity and discontinuity above for the construction of appropriate [[neighborhood (mathematics)\|neighbourhoods]], {{nowrap\|where <math>f</math> has}} maxima.