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DOI: 10.4230/OASIcs.CCA.2009.2265

Uniqueness, Continuity, and Existence of Implicit Functions in Constructive Analysis

Authors: Hannes Diener and Peter Schuster

Published in: OASIcs, Volume 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09) (2009)

Abstract

We extract a quantitative variant of uniqueness from the usual hypotheses of the implicit functions theorem. This leads not only to an a priori proof of continuity, but also to an alternative, fully constructive existence proof.

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Hannes Diener and Peter Schuster. Uniqueness, Continuity, and Existence of Implicit Functions in Constructive Analysis. In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 131-140, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{diener_et_al:OASIcs.CCA.2009.2265,
  author =	{Diener, Hannes and Schuster, Peter},
  title =	{{Uniqueness, Continuity, and Existence of Implicit Functions in Constructive Analysis}},
  booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
  pages =	{131--140},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-12-5},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{11},
  editor =	{Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2265},
  URN =		{urn:nbn:de:0030-drops-22651},
  doi =		{10.4230/OASIcs.CCA.2009.2265},
  annote =	{Keywords: Implicit function, uniqueness, continuity, constructive analysis, countable choice}
}

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Uniqueness, Continuity, and Existence of Implicit Functions in Constructive Analysis

Abstract

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