Metrizability of the strong dual: equivalent topological characterizations

Authors

  • Subiman Kundu Former Professor, Department of Mathematics Indian Institute of Technology Delhi, New Delhi 110016, India
  • Varun Jindal Department of Mathematics, Malaviya National Institute of Technology Jaipur, Jaipur, Rajasthan 302017, India

DOI:

https://doi.org/10.17398/2605-5686.40.2.173

Keywords:

Locally convex space, dual space, bounded sets, strong topology, metrizability

Abstract

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.

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References

[1] A.V. Arhangel’skiı̆, M. Tkachenko, “Topological groups and related structures”, Atlantis Stud. Math., 1, Atlantis Press, Paris; World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2008.

[2] G. Gruenhage, Generalized metric spaces, in: “Handbook of set-theoretic topology” (Edited by Kenneth Kunen and Jerry E. Vaughan), North-Holland Publishing Co., Amsterdam, 1984, 423 – 501.

[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, 2011.

[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, NY, 1995.

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Published

2025-12-17

Issue

Section

Functional Analysis and Operator Theory

How to Cite

Metrizability of the strong dual: equivalent topological characterizations. (2025). Extracta Mathematicae, 40(2), 173-179. https://doi.org/10.17398/2605-5686.40.2.173