List questions from examples-counterexamples

Published on 17 Apr 2026 - 9:03

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Is Thomas' Corkscrew completely regular? (from Counterexamples in Topology)

Published on 17 Apr 2026 - 2:03

132

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Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.

Published on 16 Apr 2026 - 9:32

43

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Are there an completely regular, non-Lindelöf spaces with only constant real valued functions?

Published on 11 Apr 2026 - 14:48

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Dimension is local on irreducible components

Published on 15 Apr 2026 - 20:48

398

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Counter example for Random variable

Published on 11 Apr 2026 - 3:37

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Explain to me this example that shows $L^1([a,b])$ is not closed under multiplication.

Published on 16 Apr 2026 - 3:22

197

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Localization of an additive category which is no longer additive

Published on 14 Apr 2026 - 10:14

123

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Orthonormal basis of $\mathbb{R}^n$ containing $v_1 = \frac{1}{\sqrt{n}}(1,1,\ldots,1)$

Published on 16 Apr 2026 - 21:54

363

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Law of large numbers: second moment tends to 0, but $S_n/n$ doesn't converge a.e.

Published on 13 Apr 2026 - 15:00

44

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Proving that a certain sequence is bounded from above

Published on 14 Apr 2026 - 13:47

1.7k

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Proving/Disproving set identity $(A\cap B)\cup C= A\cap (B\cup C)$

Published on 14 Apr 2026 - 22:01

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smooth in one direction, nowhere differentiable in the other

Published on 14 Apr 2026 - 8:35

66

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Find more counterexample mathematically or algorithmically

Published on 17 Apr 2026 - 11:07

291

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Lindelöf property and $\omega$-covers

Published on 16 Apr 2026 - 6:00

List Question

prove or disprove that $CL(A∩B)=CL(A)∩CL(B)$

Is Thomas' Corkscrew completely regular? (from Counterexamples in Topology)

Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.

Are there an completely regular, non-Lindelöf spaces with only constant real valued functions?

Dimension is local on irreducible components

Counter example for Random variable

Explain to me this example that shows $L^1([a,b])$ is not closed under multiplication.

Localization of an additive category which is no longer additive

Orthonormal basis of $\mathbb{R}^n$ containing $v_1 = \frac{1}{\sqrt{n}}(1,1,\ldots,1)$

Law of large numbers: second moment tends to 0, but $S_n/n$ doesn't converge a.e.

Proving that a certain sequence is bounded from above

Proving/Disproving set identity $(A\cap B)\cup C= A\cap (B\cup C)$

smooth in one direction, nowhere differentiable in the other

Find more counterexample mathematically or algorithmically

Lindelöf property and $\omega$-covers

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