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Fort space on real numbers is not cozero complemented - #1072

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prabau merged 4 commits into
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fort-space-cozero-complemented
Dec 12, 2024
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prabau merged 4 commits into
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fort-space-cozero-complemented

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@Moniker1998

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@Moniker1998 Moniker1998 changed the title Fort space on real numbers is not cozero complemented #1068 Fort space on real numbers is not cozero complemented Dec 12, 2024
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Moniker1998 requested a review from prabau December 12, 2024 05:32
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prabau commented Dec 12, 2024 •

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I think we should add a separate paragraph like the following at the beginning:

"Note that in any normal space the cozero sets are exactly the open $F_\sigma$-sets (Corollary 1.5.13 of {{Engelking ...}}). This is the case in $X$ since {S154|P13}."

Then the second sentence of the next paragraph can be simplified slightly:

"Then $U$ is an open $F_\sigma$-set in $X$ and hence a cozero set."

And in the refs: section, replace the existing ref with Engelking.

@Moniker1998

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@prabau what do you mean by {{Engelking ...}} ?

@GeoffreySangston

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@Moniker1998 I believe change {{Engelking : ...}} to {{zb:0684.54001}}.

In github dot dev, you can use the search feature to find other examples of this usage to confirm the style is correct. I.e., type in: {{zb

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@prabau ready for review

@prabau
prabau merged commit 1668683 into main Dec 12, 2024
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prabau deleted the fort-space-cozero-complemented branch December 12, 2024 19:39
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3 participants