List questions from examples-counterexamples

Published on 09 Apr 2026 - 15:26

564

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Primality test for numbers of the form $(11^p-1)/10$

Published on 09 Apr 2026 - 15:26

102

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Compare the topology of pointwise convergence with the vector topology in the space of the continuous scalar functions $C(I)$

Published on 13 Apr 2026 - 15:12

307

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Same homology but different fundamental group

Published on 11 Apr 2026 - 8:37

97

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A field theory Example for Luroth's Theorem

Published on 04 May 2026 - 21:10

122

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Prove that $X_1\cup X_2$ is path connected if and only if both $X_1$ and $X_2$ are path connected

Published on 15 Apr 2026 - 9:37

134

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Primality test for numbers of the form $(10^p-1)/9$ (and maybe $((10 \cdot 2^n)^p-1)/(10 \cdot 2^n-1)$)

Published on 09 Apr 2026 - 15:24

170

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Maximal Ideals of Different Heights

Published on 11 Apr 2026 - 20:54

130

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Let $B$ be a countable set and let $f$ be a surjective function ($f:A\to B$), then $A$ is also countable

Published on 14 Apr 2026 - 23:38

772

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Is $f(x,y)$ differentiable on some neighborhood of $(x_0,y_0) ?$

Published on 15 Apr 2026 - 23:36

110

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Hausdorff Quasi-Polish spaces

Published on 09 Apr 2026 - 16:18

131

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Example of a non-Lipschitz $f \in \mathrm{C}^1(U)$ where $U \subseteq \mathbb{R}^n$ is a non-convex compact connected set

Published on 15 Apr 2026 - 6:08

33

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About piecewise function without the heaviside step function .

Published on 11 Apr 2026 - 19:13

50

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Does there exist any $T \in \mathcal L (\mathcal H)$ such that $0 \lt \dim \text {ker}\ T \lt \infty$ but $\text {ran}\ T$ is not closed?

Published on 13 Apr 2026 - 0:10

162

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Example of a non-injective bounded linear operator whose range is not closed but dense.

Published on 10 Apr 2026 - 12:29

List Question

Primality test for numbers of the form $(3^p-1)/2$

Primality test for numbers of the form $(11^p-1)/10$

Compare the topology of pointwise convergence with the vector topology in the space of the continuous scalar functions $C(I)$

Same homology but different fundamental group

A field theory Example for Luroth's Theorem

Prove that $X_1\cup X_2$ is path connected if and only if both $X_1$ and $X_2$ are path connected

Primality test for numbers of the form $(10^p-1)/9$ (and maybe $((10 \cdot 2^n)^p-1)/(10 \cdot 2^n-1)$)

Maximal Ideals of Different Heights

Let $B$ be a countable set and let $f$ be a surjective function ($f:A\to B$), then $A$ is also countable

Is $f(x,y)$ differentiable on some neighborhood of $(x_0,y_0) ?$

Hausdorff Quasi-Polish spaces

Example of a non-Lipschitz $f \in \mathrm{C}^1(U)$ where $U \subseteq \mathbb{R}^n$ is a non-convex compact connected set

About piecewise function without the heaviside step function .

Does there exist any $T \in \mathcal L (\mathcal H)$ such that $0 \lt \dim \text {ker}\ T \lt \infty$ but $\text {ran}\ T$ is not closed?

Example of a non-injective bounded linear operator whose range is not closed but dense.

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