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


Dec
31
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?
Dec
30
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.
Dec
30
revised Is every fiber-preserving map between coverings again a covering?
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Dec
30
comment Is every fiber-preserving map between coverings again a covering?
@Sigur, ah I see. Thanks!
Dec
30
answered Is every fiber-preserving map between coverings again a covering?
Dec
30
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.
Dec
29
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.
Dec
28
comment Understanding induced representations
Why is $K[G] \otimes_{K[H]} V$ unintuitive to you?
Dec
27
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.
Dec
25
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 $a,b,c$
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Dec
25
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 $a,b,c$
Dec
24
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.
Dec
23
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 $xy+yz+zx \ge 3$.
Dec
22
comment Is noetherianity a local property?
@PeteL.Clark, Ah, thanks! That was what I was thinking of indeed.
Dec
22
comment Is noetherianity a local property?
@BenjaLim, I believe that they are equivalent.
Dec
18
comment On convergence of nets in a topological space
@BrianM.Scott, Excellent! Thanks.
Dec
18
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.
Dec
18
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?
Dec
18
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/…
Dec
18
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.