Borrey, S.; Schikhof, W. H. Weak and strong \(c'\)-compactness in non-Archimedean Banach spaces. (English) Zbl 0812.46077 Simon Stevin 67, Suppl., 55-58 (1993). Summary: Throughout \({\mathbf K}\) is a non-archimedean complete valued field with dense valuation \(|\cdot|\). An absolutely convex set \(A\) of a \({\mathbf K}\)-Banach space \(E\) is called (weakly) \(c'\)-compact if \(\max_{x\in A} p(x)\) exists for each (weakly) continuous seminorm \(p\) on \(E\). Assuming the continuum hypothesis, we prove that, if \({\mathbf K}\) has the cardinality of the continuum, in a strongly polar \({\mathbf K}\)- Banach space, each weakly \(c'\)-compact set is \(c'\)-compact. Cited in 2 Documents MSC: 46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis Keywords:weakly \(c'\)-compact; non-archimedean complete valued field with dense valuation; strongly polar \({\mathbf K}\)-Banach space PDFBibTeX XMLCite \textit{S. Borrey} and \textit{W. H. Schikhof}, Simon Stevin 67, 55--58 (1993; Zbl 0812.46077)