P-adic Spaces of Continuous Functions I
Annales mathématiques Blaise Pascal, Volume 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
Keywords: Non-Archimedean fields, zero-dimensional spaces, locally convex spaces
Athanasios Katsaras 1

1 Department of Mathematics University of Ioannina Ioannina, 45110 Greece
@article{AMBP_2008__15_1_109_0,
     author = {Athanasios Katsaras},
     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},
     mrnumber = {2418016},
     zbl = {1158.46050},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.242/}
}
TY  - JOUR
TI  - P-adic Spaces of Continuous Functions I
JO  - Annales mathématiques Blaise Pascal
PY  - 2008
DA  - 2008///
SP  - 109
EP  - 133
VL  - 15
IS  - 1
PB  - Annales mathématiques Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.242/
UR  - https://www.ams.org/mathscinet-getitem?mr=2418016
UR  - https://zbmath.org/?q=an%3A1158.46050
UR  - https://doi.org/10.5802/ambp.242
DO  - 10.5802/ambp.242
LA  - en
ID  - AMBP_2008__15_1_109_0
ER  - 
%0 Journal Article
%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 https://doi.org/10.5802/ambp.242
%R 10.5802/ambp.242
%G en
%F AMBP_2008__15_1_109_0
Athanasios Katsaras. P-adic Spaces of Continuous Functions I. Annales mathématiques Blaise Pascal, Volume 15 (2008) no. 1, pp. 109-133. doi : 10.5802/ambp.242. https://ambp.centre-mersenne.org/articles/10.5802/ambp.242/

[1] J. Aguayo; N. De Grande-De Kimpe; S. Navarro 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] 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 (Contemp. Math.), Volume 384, Amer. Math. Soc., Providence, RI, 2005, pp. 15-37 | MR | Zbl

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

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

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

Cited by Sources: