List questions from examples-counterexamples

Published on 13 May 2020 - 17:58

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Completely metrizable subspaces and $G_\delta$ in Hausdorff spaces

Published on 13 May 2020 - 21:12

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An example of linear transformation not matrix transformation

Published on 14 May 2020 - 2:03

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If a quotient of smooth functions can be continuously extended to a singularity, is the extension automatically smooth?

Published on 27 Mar 2026 - 16:25

638

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Is the derivative always nonnegative in a neighbourhood of a minimum?

Published on 27 Mar 2026 - 2:37

142

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Is a smooth function convex near a strict minimum?

Published on 03 Apr 2026 - 2:33

258

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Conjecture about Jensen's inequality and polynomials

Published on 25 Mar 2026 - 22:09

136

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$T_1$ spaces where the closure of a compact set is not compact

Published on 16 May 2020 - 21:09

72

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Existence of a simple homeomorphism

Published on 17 May 2020 - 10:11

87

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Example of a polynomial with a lesser degree than the minimal monic polynomial.

Published on 19 May 2020 - 23:24

596

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When does a universal cover exists for a Topological Space?

Published on 27 Mar 2026 - 20:30

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If $A$ and $B$ are $2\times 2$ matrices such that $A^2 - B^2$ is invertible, is $A-B$ invertible?

Published on 01 Apr 2026 - 19:46

74

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Are there two sets $X$ and $Y$ such that the following inequality for box dimension holds

Published on 23 Feb 2026 - 19:24

940

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Must continuous $H^1(\mathbb{R}^2)$ function tend to zero at infinity?

Published on 26 Mar 2026 - 9:38

82

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Can $\frac{\mathrm d}{\mathrm dx}$ increase the support of a function?

Published on 27 Mar 2026 - 19:32

List Question

About metric space

Completely metrizable subspaces and $G_\delta$ in Hausdorff spaces

An example of linear transformation not matrix transformation

If a quotient of smooth functions can be continuously extended to a singularity, is the extension automatically smooth?

Is the derivative always nonnegative in a neighbourhood of a minimum?

Is a smooth function convex near a strict minimum?

Conjecture about Jensen's inequality and polynomials

$T_1$ spaces where the closure of a compact set is not compact

Existence of a simple homeomorphism

Example of a polynomial with a lesser degree than the minimal monic polynomial.

When does a universal cover exists for a Topological Space?

If $A$ and $B$ are $2\times 2$ matrices such that $A^2 - B^2$ is invertible, is $A-B$ invertible?

Are there two sets $X$ and $Y$ such that the following inequality for box dimension holds

Must continuous $H^1(\mathbb{R}^2)$ function tend to zero at infinity?

Can $\frac{\mathrm d}{\mathrm dx}$ increase the support of a function?

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