# From Bolzano-Weierstraß to Arzelà-Ascoli

```@article{Kreuzer2014FromBT,
title={From Bolzano-Weierstra{\ss} to Arzel{\`a}-Ascoli},
author={Alexander P. Kreuzer},
journal={Math. Log. Q.},
year={2014},
volume={60},
pages={177-183}
}```
• 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