/sci/ - Science & Math

>>11011986
No, these are excerpts from the manga "Wild and Hausdorff Hermiticity".

>>10957810
It's called "Wild and Hausdorff Hermiticity".

>>10336499
My compatriot of dark complexion.

Here's some more Touhou maths OC

>>9691615
[math]d(e^z) = e^z dz[/math] so [eqn]4\oint_C dz e^z \cos(e^z) = 4\oint_{\ln(C)}d(e^z)\cos(e^z) = 4\oint_{w(C)}dw \cos(w)[/eqn]
where [math]w:\mathbb{C}\rightarrow \mathbb{C}[/math] is the homomorphism on cycles [math]C_1(\mathbb{C},\mathbb{Z})[/math] induced by the conformal mapping [math]z\mapsto e^z[/math].
>>9692304
[math]\otimes[/math] is tensor product, and [math]\odot[/math] is symmetrized tensor product. [eqn]X\odot Y = \frac{1}{2}\left(X\otimes Y + Y\otimes X\right)[/eqn]
>>9692377
Complements of open sets are supposed to be closed, but in the first example the complement [math]U^c = \emptyset[/math] of the neighborhood [math]U \ni c[/math] of [math]c[/math] is open.
For the second example try taking the complement of the union of the intersections of the three neighborhoods.