Problems as Solutions

  • Peter Schuster
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)


If a continuous function on a complete metric space has approximate roots and in a uniform manner at most one root, then it actually has a root. We validate this heuristic principle in Bishop–style constructive mathematics without countable choice, following Richman’s way of defining the completion of a metric space as the set of all locations.

MSC (2000): Primary 03F60; Secondary 03E25, 26E40, 54E50.


Metric spaces completeness uniform continuity unique existence constructive mathematics countable choice 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Peter Schuster
    • 1
  1. 1.Mathematisches Institut, Universität München, Theresienstr. 39, 80333 MünchenGermany

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