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user7090
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20 votes
2 answers
4k views

Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$

14 votes
5 answers
2k views

For every rational number, does there exist a sequence of irrationals which converges to it?

10 votes
5 answers
5k views

Example of two open balls such that the one with the smaller radius contains the one with the larger radius.

9 votes
2 answers
123 views

If $u\in L^1(0,1)$ is nonnegative and $E_n = \int_0^1 x^n u(x) \, dx$, prove $E_{n-k} E_k \leq E_0 E_n$.

9 votes
1 answer
1k views

Fibre of a sheaf of $\mathcal{O}_X$-modules.

8 votes
1 answer
901 views

Geometric significance of completion of a ring

8 votes
2 answers
243 views

When considering a finite-type scheme as a ringed space, is it enough to look at its $k$-points?

8 votes
1 answer
453 views

Sets of measure zero and the Lebesgue differentiation theorem.

7 votes
2 answers
823 views

How does the failure of integral closure of a coordinate ring relate to the cusp/singularity we see in the corresponding variety?

7 votes
1 answer
1k views

Example of two atlases on a manifold $M$ which give rise to different sets of smooth functions on $M$.

6 votes
1 answer
4k views

The Line with two origins

6 votes
1 answer
7k views

Homeomorphism between punctured plane and cylinder [duplicate]

5 votes
0 answers
189 views

Direct sum of cohomology rings. How to interpret?

5 votes
2 answers
2k views

Proof that an affine scheme is quasi compact [duplicate]

5 votes
1 answer
414 views

Showing that $X \times \mathbb{A}^1$ is regular in codimension one.

5 votes
0 answers
351 views

Definition of Exterior Algebra of a Graded Module

5 votes
1 answer
455 views

Moduli of Riemann surfaces (genus g curves) is a variety.

5 votes
1 answer
98 views

Definition of module of Kähler differentials for a DG algebra

4 votes
2 answers
254 views

Geodesics in the upper half plane

4 votes
1 answer
156 views

$k$-rational points of the automorphism functor of a scheme

4 votes
1 answer
387 views

Hartshorne Corollary 9.4 precise meaning of $\mathcal{F}_y$ and $\mathcal{F} \otimes k(y)$

4 votes
1 answer
325 views

How does the following define a hermitian structure?

4 votes
1 answer
3k views

A definition of a very ample divisor

4 votes
1 answer
285 views

Why are holomorphic vector bundles over $\mathbb{C}^n$ trivial?

4 votes
1 answer
532 views

Isomorphism classes of $\mathbb{Z}[i]$ modules.

4 votes
0 answers
62 views

For a $3$-by-$3$ matrix, find $A$, $B$ integer $3$-by-$3$ matrices with determinant $\pm 1$ such that $AMB$ is diagonal.

4 votes
3 answers
577 views

Finite Union of Compact Sets Clarification

3 votes
3 answers
3k views

Radius of Convergence for analytic functions

3 votes
1 answer
1k views

Prove that the set of lines in the plane is equal in cardinality to $\mathbb{R}$

3 votes
2 answers
8k views

Commutator subgroup of a dihedral group.

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