Proposition 5.15.2`0E4FD8AF1256`

Proposition 5.15.2.0E4FD8AF1256 The plurifine topology on $\Omega $ is finer than the Euclidean topology.

Proof. It suffices to show that the unit ball $\{ z\in \mathbb {C}^ n:|z|<1\} $ is $\mathcal{F}$-open. This follows from the observation that this set can be written as

\[ \{ \psi <0\} \quad \textup{with}\quad \psi (z)\coloneqq (\log |z|) \lor (-1). \]

This completes the proof. $\square$

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BibTeX citation

@misc{pome-tag-0E4FD8AF1256,
  author = {{Pome contributors}},
  title = {Proposition 5.15.2},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/0E4FD8AF1256/}
}

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Proposition 5.15.20E4FD8AF1256

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Proposition 5.15.2`0E4FD8AF1256`