List questions from examples-counterexamples

Published on 25 Mar 2026 - 23:10

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what would be an example of a function such that $\int_{|z|=r} f(z)=0$ for all $r>0$, but not analytic everywhere?

Published on 16 Jun 2014 - 16:56

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Example of a Problem Made Easier with Skew Coordinates

Published on 27 Mar 2026 - 8:41

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If $|\operatorname{Aut}_KF|=3$, must we have cube roots of unity?

Published on 17 Jun 2014 - 17:51

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WHat would be an example of this function?

Published on 18 Jun 2014 - 11:49

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Various convergences in the space of bounded operators

Published on 26 Mar 2026 - 22:53

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Difference between being faithful and being injective on arrows

Published on 19 Jun 2014 - 5:40

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If $\sum a_n$ with $a_n>0$ is convergent, then is $\sum {a_n}^2$ and $\sum \sqrt{a_n}$ always convergent?

Published on 20 Jun 2014 - 8:06

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Counterexample: Convergence in finite dimensional distributions does not imply weak convergence

Published on 30 Mar 2026 - 5:01

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Quotient of a locally compact space

Published on 26 Mar 2026 - 9:41

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Path-connected and locally connected space that is not locally path-connected

Published on 23 Mar 2026 - 2:30

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$H^1(X) = [X,\mathbb{T}]$?

Published on 22 Jun 2014 - 4:42

788

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is $\mathbb{R}^2\setminus \{(0,0)\}$ homeomorphic to $S^1$?

Published on 23 Jun 2014 - 12:56

294

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Counterexample for Palais-Smale condition

Published on 23 Jun 2014 - 15:51

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Does paracompact Hausdorff imply perfectly normal?

Published on 23 Feb 2026 - 1:02

List Question

Are surjective order-homomorphisms necessarily complete lattice homomorphisms?

what would be an example of a function such that $\int_{|z|=r} f(z)=0$ for all $r>0$, but not analytic everywhere?

Example of a Problem Made Easier with Skew Coordinates

If $|\operatorname{Aut}_KF|=3$, must we have cube roots of unity?

WHat would be an example of this function?

Various convergences in the space of bounded operators

Difference between being faithful and being injective on arrows

If $\sum a_n$ with $a_n>0$ is convergent, then is $\sum {a_n}^2$ and $\sum \sqrt{a_n}$ always convergent?

Counterexample: Convergence in finite dimensional distributions does not imply weak convergence

Quotient of a locally compact space

Path-connected and locally connected space that is not locally path-connected

$H^1(X) = [X,\mathbb{T}]$?

is $\mathbb{R}^2\setminus \{(0,0)\}$ homeomorphic to $S^1$?

Counterexample for Palais-Smale condition

Does paracompact Hausdorff imply perfectly normal?

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