Spherical completeness of the non-archimedean ring of colombeau generalized numbers
by Eberhard Mayerhofer  

Vol. 2 No. 3 (2007) P.769~P.783

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.

KEYWORDS
generalized functions, Colombeau theory, ultrametric spaces, spherically complete, topological rings, Hahn-Banach theorem

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 46F30

MILESTONES

Received: 2006-04-24
Revised : 2006-09-25
Accepted:

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