Polynomials versions of numerable type on non-archimedean locally convex spaces

  • Miguel Caldas Cueva


The purpose of this article is to present some recent developments about polynomial conditions of denumerable type barrelledness between non-archimedean locally convex spaces over a non-trivially valued field of characteristic zero.


Topological Vector Space Convex Space Metrizable Space Numerable Type Countable Union 
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  1. [1]
    Aragona J.,On The Holomorphical Classification of Spaces of Holomorphic Germs. Nagoya Math. A.84 (1981), 85–118.zbMATHMathSciNetGoogle Scholar
  2. [2]
    Bochnak J., Siciak J.,Polynomials and Multilinear Mappings in Topological Vector Spaces. Studia Math.39 (1971), 59–76.zbMATHMathSciNetGoogle Scholar
  3. [3]
    Bourbaki N.,Espaces Vectoriels Topologiques. Chapitres 1, 2, 3, 4 et 5. Hermann (1966) and (1967).Google Scholar
  4. [4]
    Bourbaki N.,Topologie Genérale, Chapitres 10. Hermann (1967).Google Scholar
  5. [5]
    Caldas M.,Uma Generalizaccão não-Arquimediana do Teorema de Mahowald para Espaccos d-Tonelados. Portugaliae Math.49 (1992), 241–247.zbMATHGoogle Scholar
  6. [6]
    Caldas M.,On Holomorphically Sequentially Barrelled and Holomorphically Sequentially Infrabarrelled Spaces. Bull. Inst. Math. Ac. Sinica18 (1990), 67–75.zbMATHGoogle Scholar
  7. [7]
    Dincen S.,Complex Analysis in Locally Convex Spaces. North Holland Math. Studies57 (1981).Google Scholar
  8. [8]
    Husain T.,Two New Classes of Locally Convex Spaces. Math. Ann166 (1966), 289–299.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Kothe G.,Topological Vector Spaces II. Springer-Verlag (1979).Google Scholar
  10. [10]
    Monna A.F.,Espaces Localement Convexes Sur Un Corps Valué. Proc. Kon. Ned. Akad. v. WetenschA62 (1959), 391–405.MathSciNetGoogle Scholar
  11. [11]
    Monna A.F.,Analyse non-Archimédienne. Ergbnisse der Math.56 (1970), Springer-Verlag.Google Scholar
  12. [12]
    Nachbin L.,Topology On Spaces of Holomorphic Mappings. Ergbnisse der Math.47 (1969), Springer-Verlag.Google Scholar
  13. [13]
    Pombo D.P.Jr.,Polynomials in Topological Vector Spaces over Valued Fields. Rend. Circ. Mat. Palermo37 (1988), 416–430.zbMATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    Pombo D.P.Jr.,On Polynomial Classification of Locally Convex Spaces. Studia Math.78 (1984), 39–57.zbMATHMathSciNetGoogle Scholar
  15. [15]
    Springer T.A.,Une Notion de Compacité dans la Théorie des Espaces Vectoriels Topologiques. Indag. Math.68 (1965), 182–189.MathSciNetGoogle Scholar
  16. [16]
    Van Der Put M., Van Tiel J.,Espaces Nucléaires non-Arquimédiens. Proc. Kon. Ned. Akad. Wtensch70 (1967), 556–561.Google Scholar
  17. [17]
    Van Tiel J.,Espaces Localement K-Convexes. Indag. Math.27 (1965), 249–289.Google Scholar

Copyright information

© Springer 1994

Authors and Affiliations

  • Miguel Caldas Cueva
    • 1
  1. 1.Departamento De Matemática AplicadaUniversidade Federal Fluminense-IMUFFNiteroiBrasi

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