Topologies polaires compatibles avec une dualité séparante sur un corps value non-archiméedien
DOI:
https://doi.org/10.4067/S0716-09172001000200006Abstract
In this paper, we deal with polar topologies in separated dual pair hX, Y i of vector spaces over a non-archimedean valued field. We study compatible polar topologies, and we give some results characterizing specific subsets of X related to these topologies, especially if the field K is spherically complete or the compatible topology is polar or strongly polar. Furthermore, we investigate some topological properties in the duality hX, Y i such as barreldness and reflexivity.References
[1] I. Fleischer, sur les espaces normés non-archimediens, Proc. Kond. Ned. Akad. V. Wetensch. A57, pp. 165-168, (1952).
[2] A. W. Ingleton, the Hahn-Banach theorem for non-archimedean valued fields, Proc. combridge Philos. Soc. 48, pp. 41-45, (1952).
[3] A. F. Monna, analyse non-archimédienne, Springer-Verlag Berlin Heidel-Berg New York, (1970).
[4] A. C. M. Rooij, non-archimedean functional analysis, Marcel Dekker, New York, (1978).
[5] H. H. Schaefer, topological vector spaces, springer-Verlag New York Heidelberg Berlin, (1971). [6] W. H. Schikhof, locally convex spaces over nonspherically complete valued I,II. Bull. soc. Math. Belg. Sér. B 38, pp. 187-224 (1986).
[7] T. A. Springer, une notion de compacité dans la théorie des espaces vectoriels topologiques, Indag. Math. 27, pp. 182-190, (1965).
[8] J. Van Tiel, Espaces localement K-convexes, I-III, Indag. Math. 27, pp. 249-289, (1965).
[2] A. W. Ingleton, the Hahn-Banach theorem for non-archimedean valued fields, Proc. combridge Philos. Soc. 48, pp. 41-45, (1952).
[3] A. F. Monna, analyse non-archimédienne, Springer-Verlag Berlin Heidel-Berg New York, (1970).
[4] A. C. M. Rooij, non-archimedean functional analysis, Marcel Dekker, New York, (1978).
[5] H. H. Schaefer, topological vector spaces, springer-Verlag New York Heidelberg Berlin, (1971). [6] W. H. Schikhof, locally convex spaces over nonspherically complete valued I,II. Bull. soc. Math. Belg. Sér. B 38, pp. 187-224 (1986).
[7] T. A. Springer, une notion de compacité dans la théorie des espaces vectoriels topologiques, Indag. Math. 27, pp. 182-190, (1965).
[8] J. Van Tiel, Espaces localement K-convexes, I-III, Indag. Math. 27, pp. 249-289, (1965).
Published
2017-04-24
How to Cite
[1]
R. A. Hassani and M. Babahmed, “Topologies polaires compatibles avec une dualité séparante sur un corps value non-archiméedien”, Proyecciones (Antofagasta, On line), vol. 20, no. 2, pp. 217-241, Apr. 2017.
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