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Let A be a subset of a normed space E. We ask the reader for a bit of patience to follow us in the proof of the following implication: \(\displaystyle {} \mathrm {If}~ A ~\mathrm {is}~\mathrm {convex},~\mathrm {then}~ \overline {A} ~\mathrm {is}~\mathrm {also}~\mathrm {convex}. \)

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Topological Vector Spaces

  • 章节

  • 发表日期：

    2025年

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  • Geraldo Botelho,
  • Daniel Pellegrino,
  • Eduardo Teixeira

摘要

Let A be a subset of a normed space E. We ask the reader for a bit of patience to follow us in the proof of the following implication: \(\displaystyle {} \mathrm {If}~ A ~\mathrm {is}~\mathrm {convex},~\mathrm {then}~ \overline {A} ~\mathrm {is}~\mathrm {also}~\mathrm {convex}. \)