R. AMEZIANE HASSANI
Université Sidi Mohamed Ben Abdellah, Fes - MAROC

and

M. BABAHMED
Université Abdelmalek Essaâdi, Tetouan - MAROC

 

Abstract

In this paper, we deal with polar topologies in separated dual pair (X, Y) 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 (X, Y) such as barreldness and reflexivity.

 

References

 

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[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 analisys, 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).

 

Received : March, 2001

R. Ameziane Hassani

Faculté des Sciences Dhar El Mehraz

Université Sidi Mohamed Ben Abdellah- FES

FES- MAROC

MAROC

E-MAIL : ramezianehassani@hotmail.com

and

Mohammed Babahmed

Departement de Mathematiques

Faculté des Sciences de Tétouan

Université Abdelmalek Essaâdi-TETOUAN

B. P. 1796 ( FES ATLAS)

FES - MAROC

MAROC

E-MAIL : babahmedmohammed@hotmail.com