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Mar
28
revised Prove that $Ker(g \otimes k)= Im(f \otimes 1_{N}) + Im (1_{M} \otimes h)$
added 409 characters in body
Mar
28
comment Rigorous pre-calc book with answers
Take a look at Knuth's Concrete Mathematics to see whether it's what you like?
Mar
28
comment If $N$ divides $a$ and $N$ divides $b$ then
But either $N\vert a$ or $N\vert b$ implies $N\vert ab$.
Mar
28
revised Trouble finding the limits of integration for polar coordinates
LaTeX
Mar
28
comment Oscillating essential discontinuities exist?
In your example $f(1/n)=(-1)^n$, the limit doesn't exist. It follows directly from $\epsilon$-$\delta$ definition. If you want to see a continuous example, try $f(x)=\sin(1/x)$ for $x\neq0$ and study $\lim_{x\to0}f(x)$.
Mar
28
revised Can anyone check if this correct?
LaTeX
Mar
28
comment Does there exist an entire function such that $f\left(n+\frac{1}{n}\right)=0$
See wiki.
Mar
28
comment Does there exist an entire function such that $f\left(n+\frac{1}{n}\right)=0$
In general, look for Weierstrass factorization.
Mar
28
asked Local normal form of a (several complex variable) holomorphic map at a point?
Mar
28
revised Proving that the tensor product is right exact
deleted 20 characters in body
Mar
28
answered Prove that $Ker(g \otimes k)= Im(f \otimes 1_{N}) + Im (1_{M} \otimes h)$
Mar
28
accepted The hyper-derived functors $\mathbb L_\bullet F$ are just derived functors of $H_0F$?
Mar
21
revised Homomorphism of local rings
added 12 characters in body
Mar
20
comment A quasi-isomorphism between the total complex of a Cartan-Eilenberg resolution and the complex per se.
@AndreaGagna I just skimmed G&M and found that they assume that the double complex is bounded. It's a different story. But the spectral sequence with filtration by rows works (assuming AB5), since it's upper half-plane therefore the spectral sequence converges to $\operatorname{Tot}^\oplus$.
Mar
13
comment The geometric interpretation for extension of ideals?
Further remarks to complete this answer: first, instead of fiber, I prefer to consider the whole morphism: $\operatorname{Spec}(A/f(I)A)\to\operatorname{Spec}(B/I)$, just like the restriction of fiber bundle into a subset. Second, I want to figure out that $A\otimes_BB/I\cong A/f(I)A$ is a corollary of the right exactness of $A\otimes_B-$, though could be checked directly.
Mar
13
revised The hyper-derived functors $\mathbb L_\bullet F$ are just derived functors of $H_0F$?
added 248 characters in body
Mar
13
answered The hyper-derived functors $\mathbb L_\bullet F$ are just derived functors of $H_0F$?
Mar
11
comment A quasi-isomorphism between the total complex of a Cartan-Eilenberg resolution and the complex per se.
@AndreaGagna Well, so only the condition that $H_n(P,d^h)$ is exact is used here? It is claimed in the text that AB5 should be assumed in the classical convergence theorem, though it seems to me that the construction and proof for everything is for modules, not generally for abelian categories. If you are right, I hope you can post an answer and I'll read it and accept it in weekends.
Mar
8
comment Long exact sequence for a triple follows from long exact sequence for a pair?
In fact, my initial idea is that the diagram chasing of the homology exact sequence of a pair could be systematized by the construction of derived couples. I guess that it's a corollary of usage of the exactness of repeated derived couples. Well, I will read your proof in the coming weekend, and sorry for my retardation.
Mar
8
comment Poincare Duality Reference
The fact that the star complexes constitutes a cellular filtration only depends on the homology of the manifold, just as Serfert & Threlfall shows. I cannot see how to determine the topology, not just homology of that, and how to take advantage of the tubular neighborhood you've mentioned. In addition, sorry for my ignorance, I don't know the tubular neighborhood theorem for triangulated manifolds, but not for differentiable manifolds.