List questions from examples-counterexamples

Published on 12 Apr 2026 - 20:44

48

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Are there any non-discrete subsets of $\mathbb{R}$ for which this "binary search game" would terminate?

Published on 13 Apr 2026 - 16:50

845

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Counter example to first countable, second countable, and separable spaces

Published on 26 Mar 2026 - 17:51

108

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Example of splitting family

Published on 12 Apr 2026 - 2:49

441

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What are some examples of free modules that have 2 bases of different sizes?

Published on 13 Apr 2026 - 4:18

11.6k

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How many times do you have to use L'Hôpital's rule?

Published on 12 Apr 2026 - 8:16

511

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$(X_n) $ a $\{F_n \}$ martingale that a.s. converges. Does this imply $\sup_n E (X_n^+) < \infty$?

Published on 16 Apr 2026 - 19:29

175

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Injective homomorphism from $\mathbb Z/q \mathbb Z$ to $\text{Aut}(\mathbb Z/p \mathbb Z)$

Published on 11 Apr 2026 - 5:13

558

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Baire's Category Theorem fails for uncountable intersection of open, dense subsets

Published on 15 Apr 2026 - 18:55

2.2k

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Are there any simple examples of Kolmogorov-Arnold representation?

Published on 11 Apr 2026 - 1:25

64

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Relations between groups and its groups algebras

Published on 09 Apr 2026 - 17:40

89

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Counterexample for uniform convergence of optimal L2 polynomial approximation

Published on 15 Apr 2026 - 22:53

450

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Do you have an example of a non trivial knot that have determinant one?

Published on 11 Apr 2026 - 2:32

413

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Prove or Disprove There Exist Only One Pair of Four Positive Integers whose sum equals their product.

Published on 15 Apr 2026 - 2:36

33

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Find $ [ S_9 : H ]$

Published on 16 Apr 2026 - 17:25

List Question

On the correspondence between normal Lie subgroup and ideal of Lie algebras.

Are there any non-discrete subsets of $\mathbb{R}$ for which this "binary search game" would terminate?

Counter example to first countable, second countable, and separable spaces

Example of splitting family

What are some examples of free modules that have 2 bases of different sizes?

How many times do you have to use L'Hôpital's rule?

$(X_n) $ a $\{F_n \}$ martingale that a.s. converges. Does this imply $\sup_n E (X_n^+) < \infty$?

Injective homomorphism from $\mathbb Z/q \mathbb Z$ to $\text{Aut}(\mathbb Z/p \mathbb Z)$

Baire's Category Theorem fails for uncountable intersection of open, dense subsets

Are there any simple examples of Kolmogorov-Arnold representation?

Relations between groups and its groups algebras

Counterexample for uniform convergence of optimal L2 polynomial approximation

Do you have an example of a non trivial knot that have determinant one?

Prove or Disprove There Exist Only One Pair of Four Positive Integers whose sum equals their product.

Find $ [ S_9 : H ]$

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