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5h
comment If a result is apparently provable with AC, is actually independent of ZF?
To say that it was first obtained by Lindenbaum and Tarski in 1926 is to skip over the actual history of the situation. Certainly it was not published in 1926, and Tarski many years later said he couldn't remember how Lindenbaum's argument for a key lemma went, but found a proof for it himself. The (Conway-)Doyle paper describes all this better than I can in a small comment box (they, or he [Doyle], surmise that they hit upon the argument Lindenbaum must have used, but I'd treat that as just a guess).
7h
comment Embedding finite lattices into the lattice of partitions of a finite set
I realize. I'll leave my answer in case it's still useful.
7h
answered Embedding finite lattices into the lattice of partitions of a finite set
1d
revised Coarsest admissible topology on $\text{Cont}(X,Y)$
fixed a link
1d
revised What technical and/or theoretical challenges are involved in automatically extracting proofs from books and papers into Coq code?
corrected spelling
1d
comment Coarsest admissible topology on $\text{Cont}(X,Y)$
@EricWofsey I'm afraid it's not immediately obvious to me. But in the key case where the base $Y$ is Sierpinski space, see section 4 of the paper by Escardó and Heckmann where they show that the Scott topology is the exponential topology.
1d
revised Coarsest admissible topology on $\text{Cont}(X,Y)$
special --> general in "adjoint functor theorem"
1d
comment Coarsest admissible topology on $\text{Cont}(X,Y)$
I was in the middle of constructing my answer before I saw your edit.
1d
answered Coarsest admissible topology on $\text{Cont}(X,Y)$
1d
comment What technical and/or theoretical challenges are involved in automatically extracting proofs from books and papers into Coq code?
In view of broadness (as mentioned by Theo), let me make this Community Wiki.
1d
comment What technical and/or theoretical challenges are involved in automatically extracting proofs from books and papers into Coq code?
You say "extracting ... to" instead of "extracting ... from", so that it's not clear to me whether you're more interested in extracting human proofs from Coq code or extracting Coq code verifications from human proofs. I'm guessing the former (?).
2d
comment To fast invert a real symmetric positive definite matrix that is almost similar to Toeplitz
Cross-posting (asking the same question on multiple sites) is frowned upon, because it can lead to duplication of effort and hence a waste of people's time. You should wait for an answer at M.SE before giving up and trying here.
Jul
2
comment The problem of finding the first digit in Graham's number
There's a 70% chance it's not $1$.
Jul
1
comment What are a couple of examples of finite sized but interesting categories?
Well, the category of finite preorders is not a finite category, so I'm not sure what you're really after. The Monster group is an interesting finite category with one object and quite a few morphisms. The poset of truth values $\{0 \leq 1\}$ has a lot of nice properties (e.g., being cartesian closed) that are worth contemplating. Something that you might wish to contemplate is why the category of finite categories does not have coequalizers!
Jun
29
comment Fields of mathematics that were dormant for a long time until someone revitalized them
Gee, I'd add the general theory of buildings to that list.
Jun
29
comment tessellation of an arbitrary shape
Cross-post: math.stackexchange.com/questions/1343867/…
Jun
29
comment Ways to prove the fundamental theorem of algebra
@DavidRoberts I really don't know. I'm having some difficulty finding the reverse mathematics of FTA through a Google search. Interesting question, though.
Jun
29
comment Good books on Geometric Theory of Dynamical Systems
As it stands, this answer is too vague to be useful. If there are books in that list that you can vouch for as being good for the OP's purpose, then you should say what they are (and why).
Jun
29
comment How to write an abstract for a math paper?
@DavidRoberts You didn't see me plagiarize!
Jun
28
comment How to write an abstract for a math paper?
Bozhe moi! (and yes, this is a good answer)