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12 votes
2 answers
678 views

Is the metric topology determined by its convergent sequences?

11 votes
3 answers
336 views

Is there a maximal ordered field? What about $\mathbb R$?

11 votes
2 answers
959 views

What form of choice is "every Dedekind-finite set is finite" equivalent to?

7 votes
3 answers
353 views

What does Paul Halmos mean here?

6 votes
1 answer
107 views

Continuously extending a function

5 votes
1 answer
72 views

Using only the universal property, prove that $X$ is dense in its Cauchy completion

5 votes
2 answers
627 views

Quantifiers in first-order logic

4 votes
5 answers
281 views

How to keep quantifiers organised in a proof?

4 votes
1 answer
229 views

How can I prove that every infinite set has a countably infinite subset using only the Axiom of Countable Choice?

4 votes
1 answer
110 views

Show that the positive solution of $a = \tanh(ax)$ satisfies $\frac{1}{1-a^2} > x$

4 votes
2 answers
341 views

Showing that $\mathbb Q$ is not a direct product of groups [duplicate]

4 votes
1 answer
107 views

Proposition 4.5.4 from Tao's Analysis II

4 votes
1 answer
491 views

A matrix manipulation from Berezin's paper

4 votes
1 answer
120 views

Problem understanding May's proof of van Kampen

4 votes
1 answer
86 views

On bijectivity of the functor $\mathsf{Set}\to\mathsf{Alg}_{\mathbb R}$

4 votes
1 answer
106 views

What are the categories whose objects form a set, called?

4 votes
1 answer
182 views

An example when $(U^\perp)^\perp = U$ but $V\ne U\oplus U^\perp$?

4 votes
1 answer
66 views

$n$-th roots in a group

4 votes
2 answers
46 views

In an open set $U$, can we always extend a disc to an open ball contained in $U$?

4 votes
1 answer
116 views

An uncertain step Paolo's proof of Eisenstein's criterion

3 votes
2 answers
72 views

Why pick this definition of measurability over this almost identical one?

3 votes
1 answer
93 views

Is there a concept of "local" measurability?

3 votes
1 answer
54 views

"Multiplicative" Archimedean property in ordered fields

3 votes
0 answers
57 views

Is my proof of the multivariate chain rule, rigorous?

3 votes
1 answer
34 views

A non-open evenly covered subset?

3 votes
2 answers
72 views

Are complements of proper subspaces dense?

3 votes
2 answers
151 views

Continuity at a point in metric spaces doesn't imply topological continuity?

3 votes
0 answers
46 views

Is this proof on neighborhoods in a increasing sequence of closed sets, incorrect?

3 votes
1 answer
173 views

A chain of well ordered sets defines a "unique" well order on the union of chains?

3 votes
2 answers
490 views

Exercise 6.7.1 of Tao’s Analysis I

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