List questions from examples-counterexamples

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Why is $\lozenge (p\to p)$ not valid in system $K$ of modal logic?

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If we restrict the character $\chi:G\to S_{o(\chi)}$, then is this map surjective?

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Is the infinite (countable or uncountable) union of disjoint closed sets closed?

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Eigenvalues of a 3x3 matrix

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Exotic Function with Log Property

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Let $N$ be a normal subgroup of finite group $G$. Prove that if order of $H$ and order of $G/N$ are relatively prime then $H$ is a subgroup of $N$.

Published on 26 Mar 2026 - 9:21

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Example of a supplemented chief factor of a group

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Examples containing all generality

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Simple Failings of Axiom of Choice in Top

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Find a counterexample: For every antiprime $n>1$, there is a prime divisor $p$ such that $n/p$ is an antiprime

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Can we say that $g$ is continuous almost everywhere?

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Counterexample of a theorem for characteristic function.

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Which countable set satisfies $\cup_{n=0}^{\infty}(\cap_{k=n}^{\infty} M_k)\neq \cap_{n=0}^{\infty}(\cup_{k=n}^{\infty} M_k)$?

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A CSA group that is not a limit group

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List Question

Example of distribution which is not come from locally integrable function

Why is $\lozenge (p\to p)$ not valid in system $K$ of modal logic?

If we restrict the character $\chi:G\to S_{o(\chi)}$, then is this map surjective?

Is the infinite (countable or uncountable) union of disjoint closed sets closed?

Eigenvalues of a 3x3 matrix

Exotic Function with Log Property

Let $N$ be a normal subgroup of finite group $G$. Prove that if order of $H$ and order of $G/N$ are relatively prime then $H$ is a subgroup of $N$.

Example of a supplemented chief factor of a group

Examples containing all generality

Simple Failings of Axiom of Choice in Top

Find a counterexample: For every antiprime $n>1$, there is a prime divisor $p$ such that $n/p$ is an antiprime

Can we say that $g$ is continuous almost everywhere?

Counterexample of a theorem for characteristic function.

Which countable set satisfies $\cup_{n=0}^{\infty}(\cap_{k=n}^{\infty} M_k)\neq \cap_{n=0}^{\infty}(\cup_{k=n}^{\infty} M_k)$?

A CSA group that is not a limit group

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