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math.FA2021
Compactness in normed spaces: a unified approach through semi-norms
Jacek Gulgowski, Piotr Kasprzak, Piotr Maćkowiak
In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms…
math.FA2021
A converse of the Banach contraction principle for partial metric spaces and the continuum hypothesis
Piotr Maćkowiak
A version of the Bessaga inverse of the Banach contraction principle for partial metric spaces is presented. Equivalence of that version and the continuum hypothesis is shown as we…