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correcting grammar as my colleague would like to refer to this post in his paper
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Tomasz Kania
Tomasz Kania
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On injectiveinjectivity of the Banach space $C_0(X)$

Let $X$ be a locally compact Hausdorff space, such that $C_0(X)$ is an injective Banach space, i.e.i.e. a $\mathfrak{P}_\lambda$ space for some $\lambda\geq 1$.

  • Is it true that $X$ is compact?

  • If additionally $X$ is a locally compact group, is it true that $X$ is finite?

On injective Banach space $C_0(X)$

Let $X$ be a locally compact Hausdorff space, such that $C_0(X)$ is an injective Banach space, i.e. a $\mathfrak{P}_\lambda$ space for some $\lambda\geq 1$.

  • Is it true that $X$ is compact?

  • If additionally $X$ is a locally compact group, is it true that $X$ is finite?

On injectivity of the Banach space $C_0(X)$

Let $X$ be a locally compact Hausdorff space, such that $C_0(X)$ is an injective Banach space, i.e. a $\mathfrak{P}_\lambda$ space for some $\lambda\geq 1$.

  • Is it true that $X$ is compact?

  • If additionally $X$ is a locally compact group, is it true that $X$ is finite?

Post Undeleted by Gerry Myerson, Emil Jeřábek, Bill Johnson
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Norbert
Norbert
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Norbert
Norbert
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  • 14
  • 27

On injective Banach space $C_0(X)$

Let $X$ be a locally compact Hausdorff space, such that $C_0(X)$ is an injective Banach space, i.e. a $\mathfrak{P}_\lambda$ space for some $\lambda\geq 1$.

  • Is it true that $X$ is compact?

  • If additionally $X$ is a locally compact group, is it true that $X$ is finite?