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In Stallings's paper

he briefly discusses how to prove "several generalizations" of Brown's theorem saying that monotone union of open $n$-cells is an open $n$-cell; however, he never formulates a precise statement of what he proves.

For the details, he refers to the paper

  • J. Stallings, On a theorem of Brown about the union of open cones, Ann. of Math, (to appear).

But as far as I can tell this paper never appeared. Does anyone know what happened and what the theorem is?

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    $\begingroup$ in a 1963 Ann. of Math. article by Stallings that paper is still cited as "to appear", however now without a journal being mentioned. $\endgroup$
    – Carlo Beenakker
    Commented Oct 6, 2021 at 21:13
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    $\begingroup$ @CarloBeenakker: Thanks for noticing that reference! I think that the lack of a journal might just be the Annals's style guide -- there are several papers in that bibliography that are "to appear", and none of them specify a journal. $\endgroup$
    – Laura
    Commented Oct 6, 2021 at 21:22
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    $\begingroup$ With regards to the publication of this paper, it looks like the journal may have been... stalling $\endgroup$
    – Sam Hopkins
    Commented Oct 7, 2021 at 2:28
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    $\begingroup$ I feel the pain. There's more than one of these in category theory from the 70s-80s, announced to appear in JPAA, but which never turned up. $\endgroup$
    – David Roberts ♦
    Commented Oct 7, 2021 at 4:02

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