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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 17th 2017
   • (edited May 17th 2017)
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   Author: Urs
   Format: MarkdownItexI was going to be lazy and follow Akhil Mathew's proof [here](https://amathew.wordpress.com/2010/08/19/a-theorem-of-michael-on-paracompactness/). But now I see that I don't follow where he wrote (way back): "I claim that the $V_\beta$ are locally finite."

   I was going to be lazy and follow Akhil Mathew’s proof here. But now I see that I don’t follow where he wrote (way back): “I claim that the $V_\beta$ are locally finite.”

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 17th 2017
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   Author: Urs
   Format: MarkdownItexIn any case, that discussion should be at _[[Michael's theorem]]_ instead. So I have added at _[[second-countable regular spaces are paracompact]]_ the statement and the easy proof as a corollary of Michael's theorem.

   In any case, that discussion should be at Michael’s theorem instead.

   So I have added at second-countable regular spaces are paracompact the statement and the easy proof as a corollary of Michael’s theorem.

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeMay 17th 2017
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   Author: Todd_Trimble
   Format: MarkdownItexRe #1: this is in the proof of Lemma 3? Is there a more precise spot in that paragraph that could can point to where you're stuck?

   Re #1: this is in the proof of Lemma 3? Is there a more precise spot in that paragraph that could can point to where you’re stuck?

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMay 17th 2017
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   Author: Urs
   Format: MarkdownItexSorry, yes. At the very end of that paragraph: The $G_\kappa$ are a _closed_ cover. To draw the conclusion at the end of the paragraph, would we not need that their interiors still cover?

   Sorry, yes. At the very end of that paragraph: The $G_\kappa$ are a closed cover. To draw the conclusion at the end of the paragraph, would we not need that their interiors still cover?