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Completions of Cauchy Vector Spaces

In: Generalized Functions, Convergence Structures, and Their Applications

Author

Listed:
  • D. C. Kent

    (Washington State University, Department of Pure and Applied Mathematics)

  • G. D. Richardson

    (University of Central Florida, Departments of Mathematics and Statistics)

Abstract

T2 and T3 completions of Cauchy vector spaces are studied. Every T2 Cauchy vector space is shown to have a strict T2 Cauchy vector space completion. A Cauchy vector space has a T3 Cauchy vector space completion exactly when the underlying Cauchy space has a T3 Cauchy space completion.

Suggested Citation

  • D. C. Kent & G. D. Richardson, 1988. "Completions of Cauchy Vector Spaces," Springer Books, in: Bogoljub Stanković & Endre Pap & Stevan Pilipović & Vasilij S. Vladimirov (ed.), Generalized Functions, Convergence Structures, and Their Applications, pages 409-414, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-1055-6_42
    DOI: 10.1007/978-1-4613-1055-6_42
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