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The problem posed by Erdos concerning this is solved by Ashutosh Kumar and Saharon Shelah: https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/fundamenta-mathematicae/all/239/3/92174/on-a-question-about-families-of-entire-functions — Preceding unsigned comment added by 193.224.79.1 (talk • contribs) 06:32, 23 May 2020 (UTC)Reply

I have no doubt that what you say is true, only...what problem? Our article on this topic says nothing about still-unsolved problems. I had to read the review on MR 3691208 to figure out what you were talking about. But I did, and added the result. —David Eppstein (talk) 07:05, 23 May 2020 (UTC)Reply

Article states: "Analytic functions" -- real analytic? Complex analytic? Does it matter? The third sentence says, I quote: .. analytic functions on a given domain with the property that, for each x in the domain, the functions in F map x to a countable set of values. Is this domain a countable set of points? Is this domain some open set? Closed set? Open sets are uncountable, so wtf? So I assume I have to guess that maybe this set {F(x)} necessarily depends on x, as otherwise analytic functions map open sets to open sets (which are uncountable). So I guess we have a different set for each x? Are there other possible interpretations of what this sentence is trying to say? I'm stumped. I'm irked that I have to jump through mental hoops just to try to guess and imagine what the third sentence is trying to say. (I mean, I think I get it now, but I doubt other readers will be so lucky.)

The third paragraph is also painful to parse, as it requires a triple-negative: Wentzel is false if CH is true, so if CH is false then Wentzel is true. But only if we revrse the sense of direction (its an equivalence, after all.) Arghh.

Finally: Erdős' proof is so short and elegant -- can we get a sketch of the proof? Some key points? Does it require points to cluster to some limit point (i.e. domains are compact)? Or is compactnesss vs non-compact utterly irrelevant to the problem? I'm trying to guess how the proof would go. Is it a proof-by-contradiction? Is it a constructive proof? 67.198.37.16 (talk) 02:55, 3 May 2025 (UTC)Reply