List questions from examples-counterexamples

Published on 28 Mar 2026 - 3:32

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Every homomorphic image of abelian group is abelian but converse need not be true.

Published on 27 Mar 2026 - 18:09

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Prime divisors of certain consecutive integers

Published on 23 Oct 2019 - 9:04

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Explicit example of non abelian group of order $pq$ where $p \mid q-1$

Published on 23 Oct 2019 - 9:55

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An example of topological space which $T_5$ but not $T_6$

Published on 25 Mar 2026 - 17:40

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Does a function that is everywhere upper semicontinuous and nowhere continuous exist?

Published on 25 Oct 2019 - 20:02

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Can a nonzero matrix be PSD and have zero trace?

Published on 26 Mar 2026 - 2:53

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Primality test for numbers of the form $N=2 \cdot 6^n+1$

Published on 26 Mar 2026 - 11:04

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How to do logical proofs with counter example

Published on 26 Oct 2019 - 16:43

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Prob. 16, Sec. 2.3, in Herstein's TOPICS IN ALGEBRA, 2nd ed: A finite set closed under an associative product with only one of the cancellation laws

Published on 27 Mar 2026 - 12:03

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Homologous paths which are not homotopic

Published on 27 Oct 2019 - 20:10

271

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Example of a nonlinear compact operator that is not continuous

Published on 25 Mar 2026 - 17:38

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On giving counterexamples in stability of non linear control systems

Published on 28 Mar 2026 - 14:07

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What's an example of a non-Hausdorff $T_1$-space which is connected, but not hyperconnected?

Published on 25 Mar 2026 - 19:05

307

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Every bounded lattice may or may not be finite.

Published on 29 Mar 2026 - 1:35

List Question

Are there any things being taught wrong?

Every homomorphic image of abelian group is abelian but converse need not be true.

Prime divisors of certain consecutive integers

Explicit example of non abelian group of order $pq$ where $p \mid q-1$

An example of topological space which $T_5$ but not $T_6$

Does a function that is everywhere upper semicontinuous and nowhere continuous exist?

Can a nonzero matrix be PSD and have zero trace?

Primality test for numbers of the form $N=2 \cdot 6^n+1$

How to do logical proofs with counter example

Prob. 16, Sec. 2.3, in Herstein's TOPICS IN ALGEBRA, 2nd ed: A finite set closed under an associative product with only one of the cancellation laws

Homologous paths which are not homotopic

Example of a nonlinear compact operator that is not continuous

On giving counterexamples in stability of non linear control systems

What's an example of a non-Hausdorff $T_1$-space which is connected, but not hyperconnected?

Every bounded lattice may or may not be finite.

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