Minimal-Hausdorff \(p\)-adic locally convex spaces. (English) Zbl 0828.46068

Summary: We characterize, in various ways, those Hausdorff locally convex spaces over a non-archimedean valued field \(K\) that do not admit a strictly weaker Hausdorff locally convex topology. Our results extend the ones obtained by N. De Grande-De Kimpe in [Indag. Math. 33, 176-180 (1971; Zbl 0209.144)], for spherically complete \(K\). For an analogous theory for compactoids instead of locally convex spaces we refer to 2nd Conf. on \(p\)-adic Functional Analysis, Santiago de Chile (1992).


46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
46A03 General theory of locally convex spaces


Zbl 0209.144
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