Geodesic
Weak bases in $p$-adic spaces
Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 3, pp. 667-676 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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We study polar locally convex spaces over a non-archimedean non-trivially valued complete field with a weak topological basis. We prove two completeness theorems and a Hahn-Banach type theorem for locally convex spaces with a weak Schauder basis. 
@article{BUMI_2002_8_5B_3_a5,
     author = {De Grande-De Kimpe, N. and K\k{a}kol, J. and Perez-Garcia, C. and Schikhof, W. H.},
     title = {Weak bases in $p$-adic spaces},
     journal = {Bollettino della Unione matematica italiana},
     pages = {667--676},
     year = {2002},
     volume = {Ser. 8, 5B},
     number = {3},
     zbl = {1072.46051},
     mrnumber = {MR1934373},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_3_a5/}
}
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%A Schikhof, W. H.
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%J Bollettino della Unione matematica italiana
%D 2002
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De Grande-De Kimpe, N.; Kąkol, J.; Perez-Garcia, C.; Schikhof, W. H. Weak bases in $p$-adic spaces. Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 3, pp. 667-676. http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_3_a5/