Metrizability of the strong dual: equivalent topological characterizations

• S. Kundu ^[1] ; Varun Jindal ^[2]
  1. [1] Indian Institute of Technology Delhi

     Indian Institute of Technology Delhi

     India

     
  2. [2] National Institute Of Technology

     National Institute Of Technology

     Japón

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 40, Nº 2, 2025, págs. 173-179
• Idioma: inglés
• DOI: 10.17398/2605-5686.40.2.173
• Enlaces
  • Texto completo
• Resumen

  • This short article presents several equivalent topological characterizations for the metrizability of the strong dual of a locally convex Hausdorff space. Among our key findings, we establish that the metrizability of the strong dual is precisely equivalent to it being a q-space

• Referencias bibliográficas
  • [1] A.V. Arhangel’skiı̆, M. Tkachenko, “Topological groups and related structures”, Atlantis Stud. Math., 1, Atlantis Press, Paris; World...
  • [2] G. Gruenhage, Generalized metric spaces, in: “Handbook of set-theoretic topology” (Edited by Kenneth Kunen and Jerry E. Vaughan), North-Holland...
  • [3] S. Lin, Z. Yun, “Generalized metric spaces and mappings”, Atlantis Stud. Math., 6, Atlantis Press, Paris, 2016.
  • [4] L. Narici, E. Beckenstein, “Topological vector spaces”, Second edition, Pure Appl. Math. (Boca Raton), 296, CRC Press, Boca Raton, FL,...
  • [5] W. Rudin, “Functional analysis”, Second edition, Internat. Ser. Pure Appl. Math., McGraw-Hill, Inc., New York, 1991.
  • [6] F. Siwiec, Generalizations of the first axiom of countability, Rocky Mountain J. Math. 5, (1975), 1 – 60.
  • [7] L.A. Steen, J.A. Seebach Jr., “Counterexamples in Topology”, Reprint of the second (1978) edition, Dover Publications, Inc., Mineola,...