List questions from examples-counterexamples

Published on 25 Sep 2014 - 23:23

100

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Example of a ring $R$ such that $R\otimes_R R\not\simeq R$

Published on 25 Mar 2026 - 1:18

23.6k

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Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?

Published on 31 Mar 2026 - 16:11

1.8k

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Does a Group being Finite Imply that It Is Cyclic?

Published on 30 Sep 2014 - 16:54

45

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Stuck trying to find unbounded $s_n$ with $\frac{1}{n}\sum_{k=1}^n s_k\rightarrow L$

Published on 03 Oct 2014 - 3:07

80

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Example of ring with two maximal ideals such that the char of the quotients is $0$, respectively $p$.

Published on 04 Oct 2014 - 14:28

1.5k

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Product of quotient maps and quotient space that is not Hausdorff

Published on 04 Oct 2014 - 19:58

83

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Ring subset which absorbs but is not an additive subgroup

Published on 06 Oct 2014 - 15:24

132

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Counterexample for existence of a minimiser in a variational problem

Published on 28 Mar 2026 - 21:27

502

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Why is a pushforward of a $\sigma$-finite measure not necessarily $\sigma$-finite?

Published on 07 Oct 2014 - 2:33

1k

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Slowly varying function without limit at infinity

Published on 27 Mar 2026 - 22:36

366

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A net in a product space and its cluster point

Published on 25 Mar 2026 - 12:48

58

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Continuity and Subspace Topology

Published on 07 Oct 2014 - 18:45

2.6k

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Suppose f : A ---> B and g : B ---> A are functions for which g o f = 1A...

Published on 08 Oct 2014 - 12:41

118

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Seeking a possible counterexample in probability.

Published on 09 Oct 2014 - 2:39

List Question

Example of differentiable function with $f'(s_{n})=0$ but $f'(0)>0$

Example of a ring $R$ such that $R\otimes_R R\not\simeq R$

Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?

Does a Group being Finite Imply that It Is Cyclic?

Stuck trying to find unbounded $s_n$ with $\frac{1}{n}\sum_{k=1}^n s_k\rightarrow L$

Example of ring with two maximal ideals such that the char of the quotients is $0$, respectively $p$.

Product of quotient maps and quotient space that is not Hausdorff

Ring subset which absorbs but is not an additive subgroup

Counterexample for existence of a minimiser in a variational problem

Why is a pushforward of a $\sigma$-finite measure not necessarily $\sigma$-finite?

Slowly varying function without limit at infinity

A net in a product space and its cluster point

Continuity and Subspace Topology

Suppose f : A ---> B and g : B ---> A are functions for which g o f = 1A...

Seeking a possible counterexample in probability.

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