Spherical Completeness of the Non-archimedean Ring of Colombeau Generalized Numbers

Abstract

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

Cite this paper

@inproceedings{Mayerhofer2006SphericalCO, title={Spherical Completeness of the Non-archimedean Ring of Colombeau Generalized Numbers}, author={Eberhard Mayerhofer}, year={2006} }