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Spherical completeness of the non-archimedean ring of Colombeau generalized numbers

Eberhard Mayerhofer
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Abstract

We show spherical completeness of the ring of Colombeau generalized real (or complex) numbers endowed with the sharp norm. As an application, we establish a Hahn Banach extension theorem for ultra pseudo normed modules (over the ring of generalized numbers) of generalized functions in the sense of Colombeau.

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Eberhard Mayerhofer. 2007-08-31. Spherical completeness of the non-archimedean ring of Colombeau generalized numbers. https://arxiv.org/abs/math/0604495

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