List questions from examples-counterexamples

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

Published on 31 Mar 2014 - 19:01

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Peculiar examples to the Stone Representation Theorem

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Function $f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ three times

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What is $\sum_{n=0}^{\infty}|a_nz^n|^2=\frac{1}{2 \pi}\int_{-\pi}^{\pi}|f(ze^{it})|^2dt$ for?

Published on 02 Apr 2014 - 16:41

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If the tensor power $M^{\otimes n} = 0$, is it possible that $M^{\otimes n-1}$ is nonzero?

Published on 27 Mar 2026 - 21:19

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Counterexample for the normalizer being a normal subgroup

Published on 28 Mar 2026 - 2:42

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example of a subgroup of index $3$ which is not normal

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Example of $\sum_i a_i\otimes b_i\in M\otimes_AN$ which cannot be written as $a\otimes b$

Published on 04 Apr 2014 - 2:41

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Inner Product on a Vector Space over a field besides $\mathbb R$ or $\mathbb C$?

Published on 04 Apr 2014 - 20:15

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Violation of the irrelevant alternative criterion of fairness in a pairwise comparison

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Lipschitz does not imply fixed points

Published on 27 Mar 2026 - 1:43

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Closed, orientable surface whose genus is very hard to find intuitively

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545

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Non-subdifferentiable convex function on a normed space

Published on 08 Apr 2014 - 4:42

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Sperners lemma how to mark internal vertices

Published on 08 Apr 2014 - 6:30

List Question

A non-closed $p$-group.

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

Peculiar examples to the Stone Representation Theorem

Function $f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ three times

What is $\sum_{n=0}^{\infty}|a_nz^n|^2=\frac{1}{2 \pi}\int_{-\pi}^{\pi}|f(ze^{it})|^2dt$ for?

If the tensor power $M^{\otimes n} = 0$, is it possible that $M^{\otimes n-1}$ is nonzero?

Counterexample for the normalizer being a normal subgroup

example of a subgroup of index $3$ which is not normal

Example of $\sum_i a_i\otimes b_i\in M\otimes_AN$ which cannot be written as $a\otimes b$

Inner Product on a Vector Space over a field besides $\mathbb R$ or $\mathbb C$?

Violation of the irrelevant alternative criterion of fairness in a pairwise comparison

Lipschitz does not imply fixed points

Closed, orientable surface whose genus is very hard to find intuitively

Non-subdifferentiable convex function on a normed space

Sperners lemma how to mark internal vertices

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