List questions from examples-counterexamples

Published on 13 Apr 2026 - 20:15

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Irreducibility of Lie algebra representations

Published on 12 Apr 2026 - 18:53

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$f$ not measurable, but $\lvert f\rvert$ measurable

Published on 16 Apr 2026 - 9:49

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Linear algebra. Find a counter-example

Published on 12 Apr 2026 - 5:02

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Counterexample to: if $1\le p<q<\infty$, then $L^q(X)\subset L^p(X)$ with $\mu(X)=\infty$

Published on 16 Apr 2026 - 20:45

221

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Example of charts on $\mathbb{R}$ that are $\mathcal{C}^r$ compatible but not $\mathcal{C}^{r+1}$ compatible.

Published on 16 Apr 2026 - 17:19

86

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For any element $e$ of an open set $V$ of a covering space, does there exist a sheet $S$ such that $e\in S\subseteq V$

Published on 13 Apr 2026 - 0:38

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A question on spaces with a point countable base?

Published on 13 Apr 2026 - 21:15

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If $G$ is a group and $N$ is a nontrivial normal subgroup, can $G/N \cong G$?

Published on 11 Apr 2026 - 13:15

2.6k

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Taking the automorphism group of a group is not functorial.

Published on 12 Apr 2026 - 0:19

1.3k

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Prove by minimum counterexample that $2^n>10n$ for $n>5$

Published on 14 Apr 2026 - 3:49

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If $A$, $B$, and $C$ are sets, the only way that $A\cup C = B \cup C$ is if $A=B$

Published on 16 Apr 2026 - 12:56

23

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Show that there exitst $f \in L^{1}([0,1])$ such that $\int_{0}^{1}f(x)g(x)dx \nrightarrow 0$

Published on 17 Apr 2026 - 0:43

483

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Ultraproducts by countably complete ultrafilter

Published on 14 Apr 2026 - 2:27

1.1k

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Isometry of a metric space with proper subset

Published on 14 Apr 2026 - 6:46

List Question

Flatness, Hilbert polynomial and reduced schemes.

Irreducibility of Lie algebra representations

$f$ not measurable, but $\lvert f\rvert$ measurable

Linear algebra. Find a counter-example

Counterexample to: if $1\le p<q<\infty$, then $L^q(X)\subset L^p(X)$ with $\mu(X)=\infty$

Example of charts on $\mathbb{R}$ that are $\mathcal{C}^r$ compatible but not $\mathcal{C}^{r+1}$ compatible.

For any element $e$ of an open set $V$ of a covering space, does there exist a sheet $S$ such that $e\in S\subseteq V$

A question on spaces with a point countable base?

If $G$ is a group and $N$ is a nontrivial normal subgroup, can $G/N \cong G$?

Taking the automorphism group of a group is not functorial.

Prove by minimum counterexample that $2^n>10n$ for $n>5$

If $A$, $B$, and $C$ are sets, the only way that $A\cup C = B \cup C$ is if $A=B$

Show that there exitst $f \in L^{1}([0,1])$ such that $\int_{0}^{1}f(x)g(x)dx \nrightarrow 0$

Ultraproducts by countably complete ultrafilter

Isometry of a metric space with proper subset

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