List questions from examples-counterexamples

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What's so cool about local compactness?

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$3\times 3$ matrix with no real eigenvalues

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Example of a continuous bijective function on and to the closure of the complex numbers, with an inverse that is not continuous?

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Give an example of a continuous strictly increasing function g:R->R which is...

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$B \subset \mathbb{R^3}$, such that $B = \rm{Fr} (\Omega)$

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Is $A^2=I \implies A=\pm I$ necessarily true?

Published on 10 Apr 2026 - 17:50

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Counter-example to Cauchy-Peano-Arzela theorem

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Does "locally connected and path-connected" imply locally path-connected?

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Submonoids of $\mathbb{N}^k$

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Non-measurable set in product $\sigma$-algebra s.t. every section is measurable.

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Closed sets, boundary, topology.

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Examples of rational equivalence.

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Uniformly integrable sequence tending to 0 a.s. but with $\mathbb{E}(\sup_n|X_n|) = \infty$

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Let $f\geq 1$, Is the function $p\rightarrow \int |f|^p d\mu$ continuous

Published on 13 Apr 2026 - 19:28

List Question

To construct a $C^{\infty}$ function such that...

What's so cool about local compactness?

$3\times 3$ matrix with no real eigenvalues

Example of a continuous bijective function on and to the closure of the complex numbers, with an inverse that is not continuous?

Give an example of a continuous strictly increasing function g:R->R which is...

$B \subset \mathbb{R^3}$, such that $B = \rm{Fr} (\Omega)$

Is $A^2=I \implies A=\pm I$ necessarily true?

Counter-example to Cauchy-Peano-Arzela theorem

Does "locally connected and path-connected" imply locally path-connected?

Submonoids of $\mathbb{N}^k$

Non-measurable set in product $\sigma$-algebra s.t. every section is measurable.

Closed sets, boundary, topology.

Examples of rational equivalence.

Uniformly integrable sequence tending to 0 a.s. but with $\mathbb{E}(\sup_n|X_n|) = \infty$

Let $f\geq 1$, Is the function $p\rightarrow \int |f|^p d\mu$ continuous

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