List questions from examples-counterexamples

Published on 17 Oct 2014 - 2:31

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A function $f$ such that the limit of $f(x^2)$ exists but not $f(x)$.

Published on 17 Oct 2014 - 13:27

671

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On convergence a.e and convergence measure

Published on 20 Oct 2014 - 4:15

1.1k

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Introductory example(s) of a functor that is full but not faithful

Published on 27 Mar 2026 - 17:52

829

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Serre fibrations vs. Hurewicz fibrations

Published on 25 Mar 2026 - 11:05

756

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Is the conjugacy map between two distinct circle homeomorphisms unique?

Published on 21 Oct 2014 - 0:18

162

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Counterexample of "the product of open subsets is open in a topological ring"?

Published on 25 Mar 2026 - 6:12

349

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Finding a counterexample: If $f=g^2$ and $f$ is differentiable on $[a,b]$, then $g$ is differentiable on $(a,b)$.

Published on 21 Oct 2014 - 23:08

791

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An abelian Banach algebra without characters

Published on 27 Mar 2026 - 2:50

494

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Embedding vs embedding as a closed subset

Published on 24 Oct 2014 - 14:06

276

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What would be an example of a magma such that $x\cdot(x\cdot x)\neq (x\cdot x)\cdot x$?

Published on 25 Oct 2014 - 7:50

512

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Visualize and define a vector space without dot / inner product

Published on 25 Oct 2014 - 11:51

39

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Question on abstract algebra about invertiblity?

Published on 26 Oct 2014 - 7:42

569

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Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.

Published on 26 Oct 2014 - 15:15

3.3k

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Example of a normal extension.

Published on 27 Oct 2014 - 11:36

List Question

An example of a group G that satisfies $x^2 =e$ , for all $x \in G$

A function $f$ such that the limit of $f(x^2)$ exists but not $f(x)$.

On convergence a.e and convergence measure

Introductory example(s) of a functor that is full but not faithful

Serre fibrations vs. Hurewicz fibrations

Is the conjugacy map between two distinct circle homeomorphisms unique?

Counterexample of "the product of open subsets is open in a topological ring"?

Finding a counterexample: If $f=g^2$ and $f$ is differentiable on $[a,b]$, then $g$ is differentiable on $(a,b)$.

An abelian Banach algebra without characters

Embedding vs embedding as a closed subset

What would be an example of a magma such that $x\cdot(x\cdot x)\neq (x\cdot x)\cdot x$?

Visualize and define a vector space without dot / inner product

Question on abstract algebra about invertiblity?

Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.

Example of a normal extension.

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