This resolves https://mathoverflow.net/questions/501062/for-what-cardinality-is-the-cofinite-topology-on-a-set-symmetrizable
I asked this question ChatGPT Pro and it came up with a construction which generalises Example 2.13 in https://ww2.ams.org/journals/tran/1976-219-00/S0002-9947-1976-0418048-0/S0002-9947-1976-0418048-0.pdf (which proves the implication for aleph1), proving the result for all cardinalities.
This also generalises the special case |X|=c proven by @yhx-12243 entirely differently.
I of course checked the proof quite carefully (attached to the issue) and it seems perfectly fine. The proof is 5 pages in preprint pdf, maybe still short enough for mathoverflow but borderline.
If I had found the proof myself, I would have also seriously considered writing a paper about the result, since it is quite surprising.
I am not saying we should just add this result immediately, but at least think of a suitable way. This is something that will happen more and more in the future and I have doubts our current model (write question on MSE) will hold up to that.
I also dont know the guidelines for AI submission of math overflow.
cofinite_symmetrizable_preprint.pdf
FYI I also tried two other problems (toronto problem and something about t2 compact weak 1st countable spaces, which it did not solve).
@prabau
This resolves https://mathoverflow.net/questions/501062/for-what-cardinality-is-the-cofinite-topology-on-a-set-symmetrizable
I asked this question ChatGPT Pro and it came up with a construction which generalises Example 2.13 in https://ww2.ams.org/journals/tran/1976-219-00/S0002-9947-1976-0418048-0/S0002-9947-1976-0418048-0.pdf (which proves the implication for aleph1), proving the result for all cardinalities.
This also generalises the special case |X|=c proven by @yhx-12243 entirely differently.
I of course checked the proof quite carefully (attached to the issue) and it seems perfectly fine. The proof is 5 pages in preprint pdf, maybe still short enough for mathoverflow but borderline.
If I had found the proof myself, I would have also seriously considered writing a paper about the result, since it is quite surprising.
I am not saying we should just add this result immediately, but at least think of a suitable way. This is something that will happen more and more in the future and I have doubts our current model (write question on MSE) will hold up to that.
I also dont know the guidelines for AI submission of math overflow.
cofinite_symmetrizable_preprint.pdf
FYI I also tried two other problems (toronto problem and something about t2 compact weak 1st countable spaces, which it did not solve).
@prabau