I'm really excited next term because I am going to be doing Riemann surfaces and learning Dobeault Cohomology! I doubt there will be that much different than singular cohomology--or is it...
I'll be giving talk to undergrads in a couple of weeks about how Hilbert's 3rd problem, which deals with cutting tetrahedra and pasting the pieces back, is solved using Hochschild cohomology
Haha. You know what I find annoying? Being of the more algebraic persuasion I really like to get into the nitty gritty of all the arguments. My advisor for this hom. alg. course is a topologist and LOVES Weibel. But, Weibel is so handwavey at times. When I try to complain to my advisor he just goes "it's obvious! Why do you need to actually construct it!"
Do you actually ever think in general abelian categories, or even if you are doing a problem in that genearlity do you just think in $R\text{-}\mathbf{Mod}$?
if $A\subseteq R\subseteq F(A)$ and you want $R$ to be $S^{-1}A$, then you need to take $S$ to be the set of elements of $A$ which are invertible in $R$, no?
if you localize A at its set of units, you just get A
ok: you have an inclusion $g:A\to R$ and every element of $S$ is mapped to an invertible element of $R$; the general theory gives you an injection $S^{-1}A\to R$
@savick01 Yes, of course, $X = \bigcup_{N=1}^\infty \bar{B}_N(x_0)$ and compact metric spaces are separable. Countable unions of countable sets are countable, too.
@RajeshD No infinite-dimensional normed space is proper.
been working on an answer. Didn't even notice I was dropped here.
Now, I've got to get ready to go to the Renaissance Faire shortly.
How is everyone here?
@JM I used Mathematica to plot a vector field to illustrate the solution to an ODE. The illustration came out looking nice; I don't know if the explanation helped at all.
@JM Which Michael? and why do people care what someone else does in LaTeX to get a particular output?
afk for a while. I will try to check in before we leave for the day.
@teddy: Don't worry, I'll learn eventually. When I tagged this one I tried to stick to the tag description: Lp spaces are normed vector spaces so it seemed to fit the tag. What I didn't think of was that you want elementary things tagged accordingly. In this case this means tagging it measure-theory instead of functional-analysis.
