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02:20
Oct 30 at 23:31, by Martin Sleziak
A new tag . A tag with this name was created and removed before.
It was supposed to say .
3
Q: A function $f$ that satisfies the Darboux property and $f:\mathbb{R}\setminus\mathbb{Q} \to \mathbb{R}$ is injective, then $f$ is continuous.

James GarrettI want to show that a function $f:\mathbb{R} \to \mathbb{R}$ that satisfies the Darboux property (Intermediate Value Theorem) and $f:\mathbb{R}\setminus\mathbb{Q} \to \mathbb{R}$ is inyective , is continuous. I know that I somehow need to use Baire’s Category Theorem, but I don’t know how. Please...

-3
Q: Why does this condition imply injectivity?

MittelGrabung62Fix $f: A\rightarrow B$ such that, for any $C \subset A$, $$f^{-1}(f(C))=C$$ I want to show that $f$ must be injective, but I do not know where to start.

 
19 hours later…
21:08
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Q: Connection between Cohen-Lenstra heuristics and related conjectures

SomeCallMeTimThe Cohen-Lenstra heuristic is a principle of arithmetic statistics saying that a finite abelian group $G$ should appear "in nature" with probability inversely proportional to $|Aut(G)|$. In Cohen and Lenstra's original paper (see here for the paper) they discuss this heuristic and related conjec...


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