Sanchez

less info
reputation
11028
bio website location age member for 2 years, 1 month seen 34 mins ago profile views 951

I really appreciate it when you take time to answer my questions. Thanks!

934 Actions

 Dec31 comment A good reference for Quadratic Forms What exactly do you have in mind when you say "nothing that goes much beyond"? What other results do you want to have/encounter in your study of geometry that needs more than canonical form? Dec30 comment Is every fiber-preserving map between coverings again a covering? @beginner, I think so. Hopefully if I didn't make mistakes again, then $\pi$ continuous and onto is sufficient to make it a covering. Dec30 revised Is every fiber-preserving map between coverings again a covering? added 310 characters in body Dec30 comment Is every fiber-preserving map between coverings again a covering? @Sigur, ah I see. Thanks! Dec30 answered Is every fiber-preserving map between coverings again a covering? Dec30 comment Is the ideal $I = \{f\mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on $[0, 1]$ a maximal ideal? @K.Ghosh, Compactness is needed for the statement that every max ideal is of the form $I_c = \{f: f(c) = 0\}$, not this one. Dec29 comment Understanding induced representations It's nice that the two answers below convinced you that induced rep is a good notion, although I'm personally curious what you mean by "there are many induced rep in contrast to restriction" - in fact I can't see how you may cook up a $G$-rep naturally from a $H$-rep other than the extension of scalars above. Dec28 comment Understanding induced representations Why is $K[G] \otimes_{K[H]} V$ unintuitive to you? Dec27 comment contractible and simply connected Consider loop 1 formed by the starting point of your free homotopy, loop 2 formed by the ending point of the free homotopy. Then at time $t$, traverse along loop 1 up to time $t$, go through the homotopy at time $t$, and come back along loop 2. This is then a based homotopy to the trivial loop at based point. Dec25 revised Prove that $\frac{a^2}{a+b}+\frac{b^2}{b+c}+\frac{c^2}{c+a}\geq\frac{1}{2}(a+b+c)$ for positive $a,b,c$ added 22 characters in body Dec25 answered Prove that $\frac{a^2}{a+b}+\frac{b^2}{b+c}+\frac{c^2}{c+a}\geq\frac{1}{2}(a+b+c)$ for positive $a,b,c$ Dec24 comment 1 dimensional representations of $S_n$ A hint for the complex number case: It suffices to show that every homomorphism $\chi: S_n$ to $\mathbb{C}^*$ is real, which then forces any such homomorphism to be either identity or sign, depending on the value at the cycle (12). To show that it's real, it suffices to show that $\chi(g) = \overline{\chi(g)}$ for any $g$, i.e. $\chi(g) = \chi(g^{-1})$. Try to show that $g$ and $g^{-1}$ are actually conjugates which lead to the result. Dec23 comment Showing that: $(\frac{a}{b+c})^2+(\frac{b}{a+c})^2+(\frac{c}{a+b})^2+\frac{10abc}{(a+b)(b+c)(c+a)}\ge 2$ This is wrong. Use AM-GM or other tools, you can show that $xy+yz+zx \ge 3$. Dec22 comment Is noetherianity a local property? @PeteL.Clark, Ah, thanks! That was what I was thinking of indeed. Dec22 comment Is noetherianity a local property? @BenjaLim, I believe that they are equivalent. Dec18 comment On convergence of nets in a topological space @BrianM.Scott, Excellent! Thanks. Dec18 comment On convergence of nets in a topological space Thanks! Is there any (succint) reference that compares nets and filters? I would like to know more about their similarities and differences. Dec18 comment On convergence of nets in a topological space I just read online that filter was another proposal to generalize sequences. Do filters capture the topology of a space in the same sense? Dec18 comment On convergence of nets in a topological space @Elias, it's net, not network if I understand your question correctly. A quick google search returns this: planetmath.org/encyclopedia/… Dec18 comment On convergence of nets in a topological space Properties defined by sequences (eg sequentially compact) are often different from those not defined by sequences (eg compact) especially in spaces that are not first countable. Nets give a more general framework that corresponds to the latter concept, e.g. compactness is equivalent to every net having a convergent subnet.