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This chapter presents unified and direct proofs of Pfister, Cascales, and Orihuela and Valdivia’s theorems about metrizability of precompact sets in \((LF)\) -spaces, \((DF)\) -spaces, and dual metric spaces, respectively. The proofs do not require the typical machinery of quasi-Suslin spaces, upper semicontinuous compact-valued maps, and so on.

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Precompact Sets in \((LM)\) -Spaces and Dual Metric Spaces

  • 章节

  • 发表日期：

    2025年

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  • Jerzy Kąkol,
  • Wiesław Kubiś,
  • Manuel López-Pellicer,
  • Damian Sobota

摘要

This chapter presents unified and direct proofs of Pfister, Cascales, and Orihuela and Valdivia’s theorems about metrizability of precompact sets in \((LF)\) -spaces, \((DF)\) -spaces, and dual metric spaces, respectively. The proofs do not require the typical machinery of quasi-Suslin spaces, upper semicontinuous compact-valued maps, and so on.