List questions from examples-counterexamples

Published on 25 Mar 2026 - 8:07

504

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Provide a counterexample: If $n^2-1$ is divisible by $5$, then $n$ is divisible by $2$ or $3$

Published on 13 Feb 2019 - 1:08

107

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Counterexample for Hausdorff Assumption is removed

Published on 13 Feb 2019 - 7:20

1.9k

Views

Intersection of path-connected sets in $\mathbb{R}^{n}$

Published on 26 Mar 2026 - 4:33

114

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Intuition behind a counterexample to $|A+A|\leq |A-A|$, where $A$ is a finite set

Published on 15 Feb 2019 - 7:56

320

Views

What matrix has only negative or zero real part for all the eigenvalues?

Published on 15 Feb 2019 - 18:42

172

Views

Doubt in Understanding Lebesgue measure.

Published on 16 Feb 2019 - 8:57

123

Views

Constructing a weird probability measure

Published on 16 Feb 2019 - 20:15

67

Views

Does there exist an open subset $A \subset [0,1]$ such that $m_(A)\neq m_(\bar{A})$?

Published on 17 Feb 2019 - 3:10

950

Views

Function in H(curl) $\cap$ H(div), but not in H1

Published on 26 Mar 2026 - 16:26

91

Views

Is every completely regular topology induced by some topological vector space?

Published on 25 Mar 2026 - 8:07

663

Views

If the dual of a topological vector space separates points, does it separate a point and a closed subspace?

Published on 25 Mar 2026 - 6:21

238

Views

For which algebra $A$: $\mathrm{vect} \cong A-$mod

Published on 25 Mar 2026 - 6:19

653

Views

Is the image of a matrix Lie group under a Lie homomorphism again a Lie group?

Published on 19 Feb 2019 - 13:14

68

Views

Why would one prove that? Counterexample needed.

Published on 19 Feb 2019 - 22:39

List Question

Is every completely regular topology induced by some proximity?

Provide a counterexample: If $n^2-1$ is divisible by $5$, then $n$ is divisible by $2$ or $3$

Counterexample for Hausdorff Assumption is removed

Intersection of path-connected sets in $\mathbb{R}^{n}$

Intuition behind a counterexample to $|A+A|\leq |A-A|$, where $A$ is a finite set

What matrix has only negative or zero real part for all the eigenvalues?

Doubt in Understanding Lebesgue measure.

Constructing a weird probability measure

Does there exist an open subset $A \subset [0,1]$ such that $m_(A)\neq m_(\bar{A})$?

Function in H(curl) $\cap$ H(div), but not in H1

Is every completely regular topology induced by some topological vector space?

If the dual of a topological vector space separates points, does it separate a point and a closed subspace?

For which algebra $A$: $\mathrm{vect} \cong A-$mod

Is the image of a matrix Lie group under a Lie homomorphism again a Lie group?

Why would one prove that? Counterexample needed.

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