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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 17th 2017
    • (edited May 17th 2017)

    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 βV_\beta are locally finite.”

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 17th 2017

    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.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 17th 2017

    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?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 17th 2017

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

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