Characterization of Fr\'echet Spaces and Application to Hausdorff MNC
Abstract
In this short note, we give a characterization of Fr\'echet spaces via properties of their metric. This allows us to prove that the Hausdorff measure of noncompactness (MNC), defined over Fr\'echet 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\'echet spaces.
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