Luxemburg, W. A. J. (1976) On a class of valuation fields introduced by A. Robinson. Israel Journal of Mathematics, 25 (3-4). pp. 189-201. ISSN 0021-2172. doi:10.1007/bf02756999. https://resolver.caltech.edu/CaltechAUTHORS:20181003-155854296
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Abstract
It is shown that the nonarchimedean valuation fields ^ρR introduced by A. Robinson are not only complete but are also spherically complete. Further-more, it is shown that to every normed linear space over the reals there exists a nonarchimedean normed linear space ^ρE over ^ρR in the sense of Monna which is spherically complete and extends E.
| Item Type: | Article | |||||||||
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| Additional Information: | © Hebrew University 1976. Dedicated to the memory of A. Robinson. Work on this paper was supported in part by NSF Grant MPS 74-17845. | |||||||||
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| Subject Keywords: | Linear Subspace; Normed Linear Space; Nonstandard Analysis; Large Natural Number; Residue Class Field | |||||||||
| Issue or Number: | 3-4 | |||||||||
| DOI: | 10.1007/bf02756999 | |||||||||
| Record Number: | CaltechAUTHORS:20181003-155854296 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20181003-155854296 | |||||||||
| Official Citation: | Luxemburg, W.A.J. Israel J. Math. (1976) 25: 189. https://doi.org/10.1007/BF02756999 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 90111 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 08 Oct 2018 17:03 | |||||||||
| Last Modified: | 16 Nov 2021 00:40 |
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