Geodesic
Metrizability of the unit ball of the dual of a quasi-normed cone
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 483-492.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We obtain theorems of metrization and quasi-metrization for several topologies of weak* type on the unit ball of the dual of any separable quasi-normed cone. This is done with the help of an appropriate version of the Alaoglu theorem which is also obtained here.
Dimostriamo teoremi di metrizzabilità e di quasi metrizzabilità per alcune topologie di tipo debole* sulla palla unitaria del duale di un cono quasi normato separabile. Ciò è ottenuto grazie a un'opportuna versione del teorema di Alaoglu, anch'essa dimostrata nel presente lavoro. 
@article{BUMI_2004_8_7B_2_a13,
     author = {Garc{\'\i}a-Raffi, L. M. and Romaguera, S. and S\'anchez-P\'erez, E. A. and Valero, O.},
     title = {Metrizability of the unit ball of the dual of a quasi-normed cone},
     journal = {Bollettino della Unione matematica italiana},
     pages = {483--492},
     publisher = {mathdoc},
     volume = {Ser. 8, 7B},
     number = {2},
     year = {2004},
     zbl = {1116.46009},
     mrnumber = {1864985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a13/}
}
TY  - JOUR
AU  - García-Raffi, L. M.
AU  - Romaguera, S.
AU  - Sánchez-Pérez, E. A.
AU  - Valero, O.
TI  - Metrizability of the unit ball of the dual of a quasi-normed cone
JO  - Bollettino della Unione matematica italiana
PY  - 2004
SP  - 483
EP  - 492
VL  - 7B
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a13/
LA  - en
ID  - BUMI_2004_8_7B_2_a13
ER  - 
%0 Journal Article
%A García-Raffi, L. M.
%A Romaguera, S.
%A Sánchez-Pérez, E. A.
%A Valero, O.
%T Metrizability of the unit ball of the dual of a quasi-normed cone
%J Bollettino della Unione matematica italiana
%D 2004
%P 483-492
%V 7B
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a13/
%G en
%F BUMI_2004_8_7B_2_a13
García-Raffi, L. M.; Romaguera, S.; Sánchez-Pérez, E. A.; Valero, O. Metrizability of the unit ball of the dual of a quasi-normed cone. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 483-492. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a13/

[1] A. R. Alimov, On the structure of the complements of Chebyshev sets, Funct. Anal. Appl., 35 (2001), 176-182. | MR | Zbl

[2] E. P. Dolzhenko-E. A. Sevast'Yanov, Sign-sensitive approximations, the space of sign-sensitive weights. The rigidity and the freedom of a system, Russian Acad. Sci. Dokl. Math., 48 (1994), 397-401. | MR | Zbl

[3] P. Fletcher-W. F. Lindgren, Quasi-Uniform Spaces, Marcel Dekker, 1982. | MR | Zbl

[4] L. M. García-Raffi-S. Romaguera-E. A. Sánchez-Pérez, Sequence spaces and asymmetric norms in the theory of computational complexity, Math. Comput. Model., 36 (2002), 1-11. | MR | Zbl

[5] L. M. García-Raffi-S. Romaguera-E. A. Sánchez-Pérez, The dual space of an asymmetric normed linear space, Quaestiones Math., 26 (2003), 83-96. | MR | Zbl

[6] K. Keimel-W. Roth, Ordered Cones and Approximation, Springer-Verlag, Berlin, 1992. | MR | Zbl

[7] R. Kopperman, Lengths on semigroups and groups, Semigroup Forum, 25 (1982), 345-360. | MR | Zbl

[8] H. P. A. Künzi, Nonsymmetric distances and their associated topologies: About the origins of basic ideas in the area of asymmetric topology, in: Handbook of the History of General Topology, C. E. Aull and R. Lowen (eds), Kluwer Acad. Publ., 3 (2001), 853-968. | MR | Zbl

[9] S. Romaguera-E. A. Sánchez-Pérez-O. Valero, Quasi-normed monoids and quasi-metrics, Publ. Math. Debrecen, 62 (2003), 53-69. | MR | Zbl

[10] S. Romaguera-M. Sanchis, Semi-Lipschitz functions and best approximation in quasi-metric spaces, J. Approx. Theory, 103 (2000), 292-301. | MR | Zbl

[11] S. Romaguera-M. Schellekens, Duality and quasi-normability for complexity spaces, Appl. Gen. Topology, 3 (2002), 91-112. | MR | Zbl

[12] R. Tix, Some results on Hahn-Banach-type theorems for continuous D-cones, Theoretical Comput. Sci., 264 (2001), 205-218. | MR | Zbl

[13] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Univ. Press, Cambridge, 1991. | MR | Zbl