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In this chapter, we show that analyticity is not a three-space property. We prove, however, that a metrizable tvs E is analytic if it contains a complete locally convex analytic subspace F such that the quotient \(E/F\) is analytic. We reprove (using Corson’s example) that the Lindelöf property is not a three-space property.

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A Three-Space Property for Analytic Spaces

  • 章节

  • 发表日期：

    2025年

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

摘要

In this chapter, we show that analyticity is not a three-space property. We prove, however, that a metrizable tvs E is analytic if it contains a complete locally convex analytic subspace F such that the quotient \(E/F\) is analytic. We reprove (using Corson’s example) that the Lindelöf property is not a three-space property.