# A mysterious paper of Stallings that was supposed to appear in the Annals

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?

• in a 1963 Ann. of Math. article by Stallings that paper is still cited as "to appear", however now without a journal being mentioned. Oct 6 at 21:13
• @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. Oct 6 at 21:22
• With regards to the publication of this paper, it looks like the journal may have been... stalling Oct 7 at 2:28
• 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. Oct 7 at 4:02