P-adic Spaces of Continuous Functions I

Athanasios Katsaras[1]

  • [1] Department of Mathematics University of Ioannina Ioannina, 45110 Greece

Annales mathématiques Blaise Pascal (2008)

  • Volume: 15, Issue: 1, page 109-133
  • ISSN: 1259-1734

Abstract

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Properties of the so called θ o -complete topological spaces are investigated. Also, necessary and sufficient conditions are given so that the space C ( X , E ) of all continuous functions, from a zero-dimensional topological space X to a non-Archimedean locally convex space E , equipped with the topology of uniform convergence on the compact subsets of X to be polarly barrelled or polarly quasi-barrelled.

How to cite

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Katsaras, Athanasios. "P-adic Spaces of Continuous Functions I." Annales mathématiques Blaise Pascal 15.1 (2008): 109-133. <http://eudml.org/doc/10549>.

@article{Katsaras2008,
abstract = {Properties of the so called $\theta _\{o\}$-complete topological spaces are investigated. Also, necessary and sufficient conditions are given so that the space $C(X,E)$ of all continuous functions, from a zero-dimensional topological space $X$ to a non-Archimedean locally convex space $E$, equipped with the topology of uniform convergence on the compact subsets of $X$ to be polarly barrelled or polarly quasi-barrelled.},
affiliation = {Department of Mathematics University of Ioannina Ioannina, 45110 Greece},
author = {Katsaras, Athanasios},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Non-Archimedean fields; zero-dimensional spaces; locally convex spaces; non-Archimedean fields; zero-dimenisonal spaces; locally convex spaces of continuous functions},
language = {eng},
month = {1},
number = {1},
pages = {109-133},
publisher = {Annales mathématiques Blaise Pascal},
title = {P-adic Spaces of Continuous Functions I},
url = {http://eudml.org/doc/10549},
volume = {15},
year = {2008},
}

TY - JOUR
AU - Katsaras, Athanasios
TI - P-adic Spaces of Continuous Functions I
JO - Annales mathématiques Blaise Pascal
DA - 2008/1//
PB - Annales mathématiques Blaise Pascal
VL - 15
IS - 1
SP - 109
EP - 133
AB - Properties of the so called $\theta _{o}$-complete topological spaces are investigated. Also, necessary and sufficient conditions are given so that the space $C(X,E)$ of all continuous functions, from a zero-dimensional topological space $X$ to a non-Archimedean locally convex space $E$, equipped with the topology of uniform convergence on the compact subsets of $X$ to be polarly barrelled or polarly quasi-barrelled.
LA - eng
KW - Non-Archimedean fields; zero-dimensional spaces; locally convex spaces; non-Archimedean fields; zero-dimenisonal spaces; locally convex spaces of continuous functions
UR - http://eudml.org/doc/10549
ER -

References

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  1. J. Aguayo, N. De Grande-De Kimpe, S. Navarro, Zero-dimensional pseudocompact and ultraparacompact spaces, -adic functional analysis (Nijmegen, 1996) 192 (1997), 11-17, Dekker, New York Zbl0888.54026MR1459198
  2. J. Aguayo, A. K. Katsaras, S. Navarro, On the dual space for the strict topology β 1 and the space M ( X ) in function space, Ultrametric functional analysis 384 (2005), 15-37, Amer. Math. Soc., Providence, RI Zbl1104.46046MR2174775
  3. George Bachman, Edward Beckenstein, Lawrence Narici, Seth Warner, Rings of continuous functions with values in a topological field, Trans. Amer. Math. Soc. 204 (1975), 91-112 Zbl0299.54016MR402687
  4. A. K. Katsaras, The strict topology in non-Archimedean vector-valued function spaces, Nederl. Akad. Wetensch. Indag. Math. 46 (1984), 189-201 Zbl0548.46059MR749531
  5. A. K. Katsaras, Bornological spaces of non-Archimedean valued functions, Nederl. Akad. Wetensch. Indag. Math. 49 (1987), 41-50 Zbl0628.46077MR883366
  6. A. K. Katsaras, On the strict topology in non-Archimedean spaces of continuous functions, Glas. Mat. Ser. III 35(55) (2000), 283-305 Zbl0970.46049MR1812558
  7. A. K. Katsaras, Separable measures and strict topologies on spaces of non-Archimedean valued functions, Bull. Belg. Math. Soc. Simon Stevin 9 (2002), 117-139 Zbl1107.46052MR2232644
  8. W. H. Schikhof, Locally convex spaces over nonspherically complete valued fields. I, II, Bull. Soc. Math. Belg. Sér. B 38 (1986), 187-207, 208–224 Zbl0615.46071MR871313
  9. A. C. M. van Rooij, Non-Archimedean functional analysis, 51 (1978), Marcel Dekker Inc., New York Zbl0396.46061MR512894

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