/sci/ - Science & Math

>>11491251
Take a sequence [math](y_n)_n \subset N_r(y')^c[/math] converging to [math]y \in (N_r(y)^c)'[/math] and enclose each of them in a neighborhood [math]N_{\epsilon_n}(y_n)[/math]. Since metric spaces are Hausdorff the fact that [math]y_n \neq x'[/math] for all [math]x'\in N_r(x)[/math] and [math]n[/math] means that you can find [math]\delta_n,\epsilon_n > 0[/math] such that [math]N_{\epsilon_n}(y_n)\cap N_{\delta_n}(x') = \emptyset[/math]. What does this tell you?

Integration is a weakly continuous linear functional

>>11321186
Apologize and explain to them briefly what made you change your mind. Assuming you applied for a position in the upcoming Fall semester that should suffice.

>>11015707
I pick the nome [math]q = \exp \tau[/math] desu.

>>10960208
ACTUALLY
https://ncatlab.org/nlab/show/geometric+realization

>>10348668
Hint: all odd-degree polynomials in [math]\mathbb{R}[x][/math] have a root in [math]\mathbb{R}[/math].

>>10143762
Virasoro algebra is the algebra of conformal generators. Let us work over the Riemann sphere [math]\mathbb{A}^1_\mathbb{C}[/math] for simplicity, such that a local coordinate neighborhood [math]\eta[/math] exists such that [math]\eta(z) = z[/math].
Let [math]\mathfrak{w}[/math] denote the Witt affine Lie algebra on [math]\mathbb{A}^1_\mathbb{C}[/math] generated by the dilation operators [math]l_n = z^n \partial, l_{-n} = z^{-z}\overline{\partial}[/math], then the Virasoro algebra is the unique central extension [math]\hat{\mathfrak{w}}[/math] that fits into the short exact sequence [math]0\rightarrow c\mathbb{C}[[z]] \rightarrow \hat{\mathfrak{w}} \rightarrow \mathfrak{w}\rightarrow 0[/math], where [math]c\mathbb{C}[[z]][/math] is the algebra of convergent Laurent series on [math]\mathbb{A}^1_\mathbb{C}[/math] and central charge [math]c[/math].

>>10086924
Reminder that
[eqn]\sum_{n\in\mathbb{Z}}f(n) = \int_\mathbb{C}f(z)\csc(\pi z)[/eqn]

>>10033566
Male as the female

>>9480652
>a spectral sequence is a sequence of pointed topological spaces
No. Sounds like what people would gather from skimming Griffith. Go read an actual QM book like Townsend, Sakurai or Landau-Lifshitz.

>>9396375
I'm researching the relation of Black Holes to concrete things such as TQFT. Currently reading Sakurai's book on Black Holes and their connections to number theory.

>>9288544
Lmao you have to show that [math]\operatorname{Im}F\phi = \operatorname{Ker}F\psi[/math]

>>9024535
A good place to start is the Landau-Lifshitz series.
1. LL classical mechanics + Goldstein
2. LL E&M + Jackson
3. LL QM + Sakurai
I'm sure you can get through this over the summer.

>>8982536
Rotations SO(3) have a universal cover of SU(2), which means that they both have the same Lie algebra and therefore the same linear (read: matrix) representation. However the algebra of su(2) is isomorphic to the Clifford algebra [math]C_{0,1}^+[/math] generated by its positive definite basis, and [math]C_{0,1}[/math] is isomorphic to the quarternions.

>>8963737
>grade school
Symplectic geometry. The geometric quantization people desperately need new talents.

>>8959978
>Stone duality
This is actually really interesting since the Gelfand duality states that the category of C*-algebras is dual to the category of cobtinuous maps on compact Hausdorff spaces. Could this point to a new class of duality a "tier" above the Stone duality that relates categories of maps on topological spaces to those of algebraic structures on posets that the Gelfand duality is part of?