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arXiv · 2005.01832

Characterization of Fr\'{e}chet Spaces and Application to Hausdorff MNC

Henning Wunderlich
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Abstract

In this short note, we give a characterization of Fr\'{e}chet spaces via properties of their metric. This allows us to prove that the Hausdorff measure of noncompactness (MNC), defined over Fr\'{e}chet spaces, is indeed an MNC. As first applications, we lift well-known fixed-point theorems for contractive and condensing operators to the setting of Fr\'{e}chet spaces.

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Henning Wunderlich. 2020-05-04. Characterization of Fr\'{e}chet Spaces and Application to Hausdorff MNC. https://arxiv.org/abs/2005.01832

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