P-adic Spaces of Continuous Functions I
Katsaras, Athanasios1
1 Department of Mathematics University of Ioannina Ioannina, 45110 Greece
Annales mathématiques Blaise Pascal, Tome 15 (2008) no. 1, pp. 109-133.

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.

DOI : 10.5802/ambp.242
Classification : 46S10, 46G10
Mots-clés : Non-Archimedean fields, zero-dimensional spaces, locally convex spaces
Katsaras, Athanasios 1

1 Department of Mathematics University of Ioannina Ioannina, 45110 Greece 
@article{AMBP_2008__15_1_109_0,
     author = {Katsaras, Athanasios},
     title = {P-adic {Spaces} of {Continuous} {Functions} {I}},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {109--133},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {15},
     number = {1},
     year = {2008},
     doi = {10.5802/ambp.242},
     zbl = {1158.46050},
     mrnumber = {2418016},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/ambp.242/}
}
TY  - JOUR
AU  - Katsaras, Athanasios
TI  - P-adic Spaces of Continuous Functions I
JO  - Annales mathématiques Blaise Pascal
PY  - 2008
SP  - 109
EP  - 133
VL  - 15
IS  - 1
PB  - Annales mathématiques Blaise Pascal
UR  - http://www.numdam.org/articles/10.5802/ambp.242/
DO  - 10.5802/ambp.242
LA  - en
ID  - AMBP_2008__15_1_109_0
ER  - 
%0 Journal Article
%A Katsaras, Athanasios
%T P-adic Spaces of Continuous Functions I
%J Annales mathématiques Blaise Pascal
%D 2008
%P 109-133
%V 15
%N 1
%I Annales mathématiques Blaise Pascal
%U http://www.numdam.org/articles/10.5802/ambp.242/
%R 10.5802/ambp.242
%G en
%F AMBP_2008__15_1_109_0
Katsaras, Athanasios. P-adic Spaces of Continuous Functions I. Annales mathématiques Blaise Pascal, Tome 15 (2008) no. 1, pp. 109-133. doi : 10.5802/ambp.242. http://www.numdam.org/articles/10.5802/ambp.242/

[1] Aguayo, J.; De Grande-De Kimpe, N.; Navarro, S. Zero-dimensional pseudocompact and ultraparacompact spaces, p-adic functional analysis (Nijmegen, 1996) (Lecture Notes in Pure and Appl. Math.), Volume 192, Dekker, New York, 1997, pp. 11-17 | MR | Zbl

[2] Aguayo, J.; Katsaras, A. K.; Navarro, S. On the dual space for the strict topology β 1 and the space M(X) in function space, Ultrametric functional analysis (Contemp. Math.), Volume 384, Amer. Math. Soc., Providence, RI, 2005, pp. 15-37 | MR | Zbl

[3] Bachman, George; Beckenstein, Edward; Narici, Lawrence; Warner, Seth Rings of continuous functions with values in a topological field, Trans. Amer. Math. Soc., Volume 204 (1975), pp. 91-112 | DOI | MR | Zbl

[4] Katsaras, A. K. The strict topology in non-Archimedean vector-valued function spaces, Nederl. Akad. Wetensch. Indag. Math., Volume 46 (1984) no. 2, pp. 189-201 | MR | Zbl

[5] Katsaras, A. K. Bornological spaces of non-Archimedean valued functions, Nederl. Akad. Wetensch. Indag. Math., Volume 49 (1987) no. 1, pp. 41-50 | MR | Zbl

[6] Katsaras, A. K. On the strict topology in non-Archimedean spaces of continuous functions, Glas. Mat. Ser. III, Volume 35(55) (2000) no. 2, pp. 283-305 | MR | Zbl

[7] Katsaras, A. K. Separable measures and strict topologies on spaces of non-Archimedean valued functions, Bull. Belg. Math. Soc. Simon Stevin, Volume 9 (2002) no. suppl., pp. 117-139 | MR | Zbl

[8] Schikhof, W. H. Locally convex spaces over nonspherically complete valued fields. I, II, Bull. Soc. Math. Belg. Sér. B, Volume 38 (1986) no. 2, p. 187-207, 208–224 | MR | Zbl

[9] van Rooij, A. C. M. Non-Archimedean functional analysis, Monographs and Textbooks in Pure and Applied Math., 51, Marcel Dekker Inc., New York, 1978 | MR | Zbl

Cité par Sources :