in the group $S_n $ prove that $H = \{ \sigma \in S_n | \sigma (n) =n \} $ is isomorphic to $S_{n-1} $ i know tis is incredibly obvious but im having trouble stating the isomorphism
@Daminark I had a friend in high school (who is now a set theory grad student) who made me read Halmos's book and straight up it almost made me give up math lol
@Daminark I think descriptive set theory is actually way more interesting. i mean, analytic issues come up. i still don't like it as much as i like other stuff though.
prove that for any $ \sigma_{1}, \sigma_{2} \in S_n$ their left cosets $\sigma_{1} H$ and $\sigma_{2}H $ are equal iff $\sigma_{1}(n) = \sigma_{2} (n)$ what exactly is this saying?
@AlessandroCodenotti I have a license, but when my parents pick me up from uni I always fall asleep on the way home, so they're probably not gonna let me drive anytime soon again
@Daminark the time Peter May subbed in for my point set topology lecturer in my first year of college he wouldn't stop talking about finite topological spaces
Ohh yeah @BalarkaSen, in the definition of a subcomplex $Y$ of a CW-Complex $X$, is the subcomplex $Y$ defined to be the subspace that is a union of cells of $X$, or disjoint union of cells of $X$ (with the appropriate further conditions)
The reading course I did with the two guys a year ago ... they did the hardest problems in Munkres and we got to a lot on covering spaces and $\pi_1$. They also corrected me when I screwed up something on their exam about quotient topology.
Good, @Balarka. @EricSilva is supposed to be learning sheaf cohomology from Chern, too.
As in, I never was in a position to take point-set topology as either an undergrad math person or as a grad physics person. So therefore it's not something I want to do
