Separating maps and the nonarchimedean Hewitt theorem

J. Araujo; E. Beckenstein; L. Narici

Annales mathématiques Blaise Pascal (1995)

  • Volume: 2, Issue: 1, page 19-27
  • ISSN: 1259-1734

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Araujo, J., Beckenstein, E., and Narici, L.. "Separating maps and the nonarchimedean Hewitt theorem." Annales mathématiques Blaise Pascal 2.1 (1995): 19-27. <http://eudml.org/doc/79115>.

@article{Araujo1995,
author = {Araujo, J., Beckenstein, E., Narici, L.},
journal = {Annales mathématiques Blaise Pascal},
keywords = {biseparating map; commutative nontrivially valued nonarchimedean field; nonarchimedean counterpart to the well-known Hewitt theorem; weighted composition map; weight function},
language = {eng},
number = {1},
pages = {19-27},
publisher = {Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal},
title = {Separating maps and the nonarchimedean Hewitt theorem},
url = {http://eudml.org/doc/79115},
volume = {2},
year = {1995},
}

TY - JOUR
AU - Araujo, J.
AU - Beckenstein, E.
AU - Narici, L.
TI - Separating maps and the nonarchimedean Hewitt theorem
JO - Annales mathématiques Blaise Pascal
PY - 1995
PB - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
VL - 2
IS - 1
SP - 19
EP - 27
LA - eng
KW - biseparating map; commutative nontrivially valued nonarchimedean field; nonarchimedean counterpart to the well-known Hewitt theorem; weighted composition map; weight function
UR - http://eudml.org/doc/79115
ER -

References

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  1. [1] J. Araujo, Distance from an isometry to the Banach-Stone maps. In p-adic Functional Analysis, edited by J. M. Bayod, N. de Grande-de Kimpe, J. Martinez-Maurica, Lect. Notes in Pure and Appl. Math.137, Dekker, New York, 1992, 1-12. Zbl0780.46041MR1152564
  2. [2] J. Araujo and J. Martínez-Maurica, The nonarchimedean Banach-Stone theorem. In p-adic Analysis, edited by F. Baldassarri, S. Bosch and B. Dwork, Lect. Notes in Math.1454, Springer-Verlag, Berlin, -Heidelberg-New York1990, 64-79. Zbl0731.46043MR1094847
  3. [3] J. Araujo and J. Martínez-Maurica, Isometries between non-Archimedean spaces of continuous functions. In Papers on General Topology and Applications, edited by S. Andima, R. Kopperman, P. Ram Misra, A. R. Todd, Annals of the New York Academy of Sciences, 659, 1992, 12-17. Zbl1251.46041MR1485265
  4. [4] G. Bachman, E. Beckenstein, L. Narici and S. Warner, Rings of continuous functions with values in a topological field. Trans. A. M. S.204 (1975), 91-112. Zbl0299.54016MR402687
  5. [5] E. Beckenstein and L. Narici, A nonarchimedean Banach-Stone theorem. Proc. A.M.S.100 (1987), 242-246. Zbl0645.46065MR884460
  6. [6] E. Beckenstein and L. Narici, Automatic continuity of certain linear isomorphisms. Acad. Royale Belg. Bull. Cl. Sci.73(5) (1987), 191-200. Zbl0664.46079MR949991
  7. [7] E. Beckenstein, L. Narici and C. Suffel, Topological algebras. Mathematics Studies24, North Holland, Amsterdam1977. Zbl0348.46041MR473835
  8. [8] E. Beckenstein, L. Narici and A.R. Todd, Automatic continuity of linear maps on spaces of continuous functions. Manuscripta Math., 62 (1988), 257-275. Zbl0666.46018MR966626
  9. [9] L. Gillman and M. Jerison, Rings of continuous functions. University Ser. in Higher Math., Van Nostrand, Princeton, N. J., 1960. Zbl0093.30001MR116199
  10. [10] E. Hewitt, Rings of real-valued continuous functions. I. Trans. A. M. S.64 (1948), 45-99. Zbl0032.28603MR26239
  11. [11] K. Jarosz, Automatic continuity of separating linear isomorphisms. Canad. Math. Bull., 33(2) (1990) 139-144. Zbl0714.46040MR1060366
  12. [12] L. Narici, E. Beckenstein and J. Araujo, Separating maps on rings of continuous functions. In p-adic Functional Analysis, edited by N. de Grande-de Kimpe, S. Navarro and W. H. Schikhof. Universidad de Santiago, Santiago, Chile, 1994, 69-82. 
  13. [13] A.C.M. van Rooij, Non-archimedean Functional Analysis. Dekker, New York1978. Zbl0396.46061MR512894
  14. [13] J. Araujo, E. Beckenstein and L. NariciBiseparating maps and homeomorphic realcompactifications to appear in J. Math. Ann. Appl. Zbl0828.47024MR1329423
  15. [14] J. Araujo, P. Fernandez-Ferreiros and J. Martinez-MauricaPseudocompact and P-spaces in non archimedean Functional Analysis p-Adic Functional Analysis, Lecture Notes in Pure and Applied Mathematics, 137. Dekker1992, pags 13-21 Zbl0780.46042MR1152565

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