ziggurism's user avatar
ziggurism's user avatar
ziggurism's user avatar
ziggurism
  • Member for 12 years, 7 months
  • Last seen this week
52 votes
1 answer
4k views

Is Zorn's lemma required to prove the existence of a maximal atlas on a manifold?

49 votes
4 answers
6k views

Natural and coordinate free definition for the Riemannian volume form?

42 votes
3 answers
2k views

is a net stronger than a transfinite sequence for characterizing topology?

40 votes
2 answers
2k views

Does Ramanujan summation evaluate the series $\sum \frac{1}{n^s}$ to $\zeta(s)$ or $\zeta(s)-\frac{1}{s-1}$?

20 votes
5 answers
5k views

Show $\lim_{h\to 0} \frac{(a^h-1)}{h}$ exists without l'Hôpital or even referencing $e$ or natural log

16 votes
2 answers
2k views

why are subobjects defined to be equivalence classes of objects, instead of just objects?

14 votes
1 answer
777 views

Can we show that $1+2+3+\dotsb=-\frac{1}{12}$ using only stability or linearity, not both, and without regularizing or specifying a summation method?

14 votes
1 answer
2k views

Why a different tensor product for left $G$-modules (group representations)?

14 votes
1 answer
2k views

Why unitary characters for the dual group in Pontryagin duality if $G$ is not compact?

13 votes
3 answers
4k views

Canonical isomorphism between $\mathfrak{so}(3)$ and $\mathbb R^3$ with vector cross product

12 votes
2 answers
531 views

Is there an intrinsic or natural topology on a field, motivating the definition of the Zariski topology

11 votes
2 answers
1k views

sign error proving product rule for the Laplacian on a product of Riemannian manifolds

10 votes
1 answer
987 views

Does the splitting lemma hold without the axiom of choice?

9 votes
2 answers
443 views

Reference for densities and pseudoforms and non-tensorial representations of $\operatorname{GL}(n)$ and associated vector bundles

7 votes
2 answers
598 views

Why is the complex domain of cosine naturally a sphere?

7 votes
2 answers
581 views

Is the axiom of induction constructively verifiable for a non-standard model of arithmetic?

7 votes
1 answer
1k views

Monoidal product is coproduct in category of commutative monoids

7 votes
2 answers
610 views

Tensor product of real line bundles is trivial as a map $\mathbb{R}P^\infty\to\mathbb{R}P^\infty\times\mathbb{R}P^\infty\to\mathbb{R}P^\infty$

6 votes
2 answers
778 views

Is the circle a rational curve and what is its function field?

6 votes
1 answer
298 views

homotopy equivalent structure groups have h.e. classifying spaces (if $G\simeq H$ then $BG\simeq BH$)

6 votes
1 answer
401 views

Is the Yoneda completion of the rationals the extended real line?

5 votes
3 answers
113 views

binomial coefficient identity $\sum_{k=0}^n {n\choose k}\sum_{j=0}^{k-1}{{n-1}\choose j}=2^{2n-2}$

5 votes
0 answers
344 views

What is the relationship between the asymptotic series outside the radius of convergence and the analytic continuation?

5 votes
0 answers
419 views

Are elements of a ring actual functions or sections on the spectrum?

5 votes
1 answer
1k views

Which is the correct universal line bundle: the tautological bundle or its dual?

5 votes
2 answers
2k views

Why is the group action on the vector space of polynomials naturally a left action?

5 votes
1 answer
1k views

Does the functoriality of the pushforward on smooth manifolds require the chain rule?

5 votes
1 answer
729 views

On what domain is the dilogarithm analytic?

5 votes
0 answers
602 views

basis free volume form for a symplectic vector space

4 votes
1 answer
469 views

Show $\sum^\infty (2n-3)!!/(2n)!!$ converges