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Non-trivial natural endomorphisms on $\operatorname{Top}$

proof-verification category-theory asked Aug 10, 2018 at 11:45

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9 votes

Can the torus and the Klein bottle be thought as $\mathbb{R}^2/G$ with $G$ a finite group acting freely

general-topology manifolds asked Oct 11, 2018 at 3:47

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8 votes

When is the submodule of a product a product of submodules?

abstract-algebra ring-theory modules asked Jul 4, 2018 at 5:50

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7 votes

$ab \equiv 1 \ (n)$ implies $a$ and $b$ coprime with $n$? [Proof Verification]

elementary-number-theory proof-verification asked Mar 23, 2018 at 22:32

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7 votes

About a specific step in a proof of the fact that filtered colimits and finite limits commute in $\mathbf{Set}$

category-theory proof-explanation limits-colimits asked Jan 16, 2019 at 9:36

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6 votes

Elementary results on Stanley-Reisner rings

commutative-algebra soft-question simplicial-complex asked Jul 9, 2020 at 7:54

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6 votes

Invertibility of $I-A^s$ for each $s \geq 1$ implying nilpotence

linear-algebra algebraic-number-theory alternative-proof nilpotence asked Jan 16, 2021 at 4:34

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6 votes

Are finite colimits closed under finite colimits?

category-theory limits-colimits asked Dec 14, 2023 at 5:05

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6 votes

A combinatorial proof of Wilson's theorem [Proof Verification]

combinatorics elementary-number-theory proof-verification proof-writing asked Apr 19, 2018 at 1:05

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6 votes

When does a bijection of topologies induce a homeomorphism of spaces?

general-topology soft-question asked Aug 31, 2018 at 4:27

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Top Answers

Why are abelian groups of interest? What is their usefulness?

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Integrating both sides of an equation: what does it really mean?

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Non-associative operations

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Determinant of matrix with $A_{ij} = \min (i, j)$

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Let $A_{n\times n}$ be a real matrix. Is it true that $I+A^TA$ is invertible?

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Does the series $\sum \frac{n!}{(2n)!}$ converge?

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If $A^k=O$ for some $k\ge 2$ does it necessarily imply that $I+A$ is invertible?

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Discontinuous function with bounded variation

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If two spaces are homeomorphic and one is a metric space must the other be as well?

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Intermediate field of $\mathbb F_9(x)/$ $\mathbb F_3(x^2)$.

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What subsets of $\Bbb R$ are closed under countable sums?

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Every finite group $H$ is a quotient of $A_n$ for some $n \geq 1$.

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Proof of the converse Borel-Cantelli lemma

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Understanding a Proof in Topology of the Reals

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An Example of a Torsion Module

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Prove that the only ring homomorphism from $\mathbb Z$ to $\mathbb Z$ is Identity mapping

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Fundamental group of discs with boundaries identified

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Tensor product of direct sums = direct sum of tensor products?

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A simpler way for proving $4^{2n+1} + 7^{2n+1}$ is divisible by $11$?

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Is every open interval a union of half open intervals?

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A finitely generated module with surjective homomorphism into $R^n$ implies kernel of the map is finitely generated.

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How do the proper ideals of $\Bbb Q[x]/ \langle x^3 \rangle$ look like?

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About the universal property of initial and final topologies

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Is it true, that every morphism in a product is a retraction?

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Construct a continuous real valued function which takes zero on integers and such that image of function is not closed.

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If I and J are two ideals, I∪J is an ideal if and only if I⊂J or J⊂I. How can we prove the subset part?

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Hatcher 2.1 problem 19 - homology of square boundary plus interior points with first coordinate rational

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Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set

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Find the field that $\mathbb{Z}_7[x,y]/\langle y-2x^2, 4xy + y +1 \rangle$ is isomorphic to

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How to show that if f^N is a contraction mapping, then f has a unique fixed point.

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