From Bolzano-Weierstraß to Arzelà-Ascoli

  title={From Bolzano-Weierstra{\ss} to Arzel{\`a}-Ascoli},
  author={Alexander P. Kreuzer},
  journal={Math. Log. Q.},
  • Alexander P. Kreuzer
  • Published 2014
  • Mathematics, Computer Science
  • Math. Log. Q.
  • We show how one can obtain solutions to the Arzela-Ascoli theorem using suitable applications of the Bolzano-Weierstras principle. With this, we can apply the results from [10] and obtain a classification of the strength of instances of the Arzela-Ascoli theorem and a variant of it. Let be the statement that each equicontinuous sequence of functions contains a subsequence that converges uniformly with the rate and let be the statement that each such sequence contains a subsequence which… CONTINUE READING

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