List questions from examples-counterexamples

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What is the spectral theorem for compact self-adjoint operators on a Hilbert space actually for?

Published on 11 Apr 2026 - 14:04

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Is $\mathbb{C}^*$ modulo the roots of unity isomorphic to $\mathbb{R}^+$?

Published on 15 Apr 2026 - 14:06

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Find examples of two series $\sum a_n$ and $\sum b_n$ both of which diverge but for which $\sum \min(a_n, b_n)$ converges

Published on 13 Apr 2026 - 19:10

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Does $R[x] \cong S[x]$ imply $R \cong S$?

Published on 12 Apr 2026 - 0:35

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Is every Lebesgue measurable function on $\mathbb{R}$ the pointwise limit of continuous functions?

Published on 09 Apr 2026 - 18:00

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Defining "Small Classes."

Published on 11 Apr 2026 - 1:59

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Continuous bijections from the open unit disc to itself - existence of fixed points

Published on 11 Apr 2026 - 6:58

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Are there any countable Hausdorff connected spaces?

Published on 11 Apr 2026 - 14:48

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Epimorphism from GL(2,Z) to GL(2,Z)

Published on 14 Apr 2026 - 6:20

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Why should I avoid the Frobenius Norm?

Published on 11 Apr 2026 - 0:13

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Good examples of double induction

Published on 14 Apr 2026 - 10:12

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Example of Intersection of Pure Subgroup which is not Pure

Published on 11 Apr 2026 - 5:17

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One dimensional boundary value problems showing interesting behaviour

Published on 10 Apr 2026 - 8:33

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What's a very simple example of an equivariant map?

Published on 13 Apr 2026 - 15:16

List Question

How are eigenvectors/eigenvalues and differential equations connected?

What is the spectral theorem for compact self-adjoint operators on a Hilbert space actually for?

Is $\mathbb{C}^*$ modulo the roots of unity isomorphic to $\mathbb{R}^+$?

Find examples of two series $\sum a_n$ and $\sum b_n$ both of which diverge but for which $\sum \min(a_n, b_n)$ converges

Does $R[x] \cong S[x]$ imply $R \cong S$?

Is every Lebesgue measurable function on $\mathbb{R}$ the pointwise limit of continuous functions?

Defining "Small Classes."

Continuous bijections from the open unit disc to itself - existence of fixed points

Are there any countable Hausdorff connected spaces?

Epimorphism from GL(2,Z) to GL(2,Z)

Why should I avoid the Frobenius Norm?

Good examples of double induction

Example of Intersection of Pure Subgroup which is not Pure

One dimensional boundary value problems showing interesting behaviour

What's a very simple example of an equivariant map?

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