In the theory of nonarchimedean normed spaces over valued fields other than R or C, the property of spherical completeness is of utmost importance in several contexts, and it appears to play the role conventional completeness does in some topics of classical functional analysis. In this note we give various characterizations of spherical completeness for general ultrametric spaces, related to but different from the notions of pseudo-convergent sequence and pseudo-limit introduced by Ostrowski in [4], and apply them to obtain some new results. Although we use the language and methods of so-called infinitesimal (or non-standard) analysis, the way to rephrase some of our statements within non-infinitesimal analysis is pointed out conveniently.
The first part contains some notations and our main result. The second part deals with some applications. In the third part, one more characterization of spherical completeness is given.
@article{urn:eudml:doc:39814,
title = {Spherical completeness with infinitesimals.},
journal = {Revista Matem\'atica Hispanoamericana},
volume = {42},
year = {1982},
pages = {3-14},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39814}
}
Bayod, José Manuel. Spherical completeness with infinitesimals.. Revista Matemática Hispanoamericana, Tome 42 (1982) pp. 3-14. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39814/