List questions from examples-counterexamples

Published on 09 May 2015 - 9:05

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Is every subgroup of a normal subgroup normal?

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All possible total orderings of a finite set are isomorphic. What are some other examples of this phenomenon?

Published on 29 Mar 2026 - 19:11

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The homotopy category of complexes

Published on 13 May 2015 - 12:28

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Are all groups algebraic?

Published on 29 Mar 2026 - 3:18

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Does one of these conditions on a sequence imply the other one?

Published on 14 May 2015 - 9:04

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Is imaged of a Polish Hausdorff space under an injecitve map always Hausdorff?

Published on 26 Mar 2026 - 22:58

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Is it true that the intersection of a sequence $K_1 \supset K_2 \supset K_3 \dotsm$ of connected subsets of $\mathbb{R}^2$ is also connected?

Published on 16 May 2015 - 11:32

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An example of a mapping $\eta\colon\mathbb{N}\to\mathbb{N}$ such that $\eta(x)=n$ has infinitely many solutions for each $n\in\mathbb{N}$

Published on 17 May 2015 - 15:18

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core-compact but not locally compact

Published on 26 Mar 2026 - 11:06

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Possible textbook redundancy concerning invertible mappings

Published on 19 May 2015 - 2:19

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Conservative field $F$ on not simple connected set

Published on 03 Apr 2026 - 20:14

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Pointwise Convergence: No Diagonal Subsequence Exists?

Published on 21 May 2015 - 6:37

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On the properties of an interesting set on the real line...

Published on 22 May 2015 - 0:37

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Can a field extension still have "non-separability" above its maximal purely inseparable subextension?

Published on 23 Feb 2026 - 12:05

List Question

Does $f\Big(x+\frac{1}{n}\Big) \to f(x)$ for a.e. x as $n \to \infty$?

Is every subgroup of a normal subgroup normal?

All possible total orderings of a finite set are isomorphic. What are some other examples of this phenomenon?

The homotopy category of complexes

Are all groups algebraic?

Does one of these conditions on a sequence imply the other one?

Is imaged of a Polish Hausdorff space under an injecitve map always Hausdorff?

Is it true that the intersection of a sequence $K_1 \supset K_2 \supset K_3 \dotsm$ of connected subsets of $\mathbb{R}^2$ is also connected?

An example of a mapping $\eta\colon\mathbb{N}\to\mathbb{N}$ such that $\eta(x)=n$ has infinitely many solutions for each $n\in\mathbb{N}$

core-compact but not locally compact

Possible textbook redundancy concerning invertible mappings

Conservative field $F$ on not simple connected set

Pointwise Convergence: No Diagonal Subsequence Exists?

On the properties of an interesting set on the real line...

Can a field extension still have "non-separability" above its maximal purely inseparable subextension?

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