List questions from examples-counterexamples

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$\lim_{n\rightarrow\infty}n(\ln n)a_n=0$ implies $\sum a_n$ converges?

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Operator which is symmetric but not associative?

Published on 09 Apr 2026 - 14:16

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Linear map between the same dimensional spaces

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A comparison between the fundamental groupoid and the fundamental group

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What's the difference between Complex infinity and undefined?

Published on 09 Apr 2026 - 14:50

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Is a perfectly normal space always a paracompact space?

Published on 12 Apr 2026 - 19:24

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Surjective and continuous map between Hausdorff spaces

Published on 12 Apr 2026 - 21:07

243

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Is every perfectly normal space submetrizable?

Published on 10 Apr 2026 - 4:22

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Is projection of a closed set $F\subseteq X\times Y$ always closed?

Published on 25 Mar 2026 - 20:36

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Constructing a separable space that is not hereditarily separable.

Published on 13 Apr 2026 - 15:18

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Examples of metric spaces which are not normed linear spaces?

Published on 12 Apr 2026 - 14:17

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A Banach algebra that cannot be represented on a Hilbert space

Published on 13 Apr 2026 - 18:01

283

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Where is the fallacy in this coupling argument of two Bernoulli variables?

Published on 20 Jun 2013 - 14:53

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Ring and Subring with different Identities

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List Question

Infinitely many zeros of a nonconstant continuous function?

$\lim_{n\rightarrow\infty}n(\ln n)a_n=0$ implies $\sum a_n$ converges?

Operator which is symmetric but not associative?

Linear map between the same dimensional spaces

A comparison between the fundamental groupoid and the fundamental group

What's the difference between Complex infinity and undefined?

Is a perfectly normal space always a paracompact space?

Surjective and continuous map between Hausdorff spaces

Is every perfectly normal space submetrizable?

Is projection of a closed set $F\subseteq X\times Y$ always closed?

Constructing a separable space that is not hereditarily separable.

Examples of metric spaces which are not normed linear spaces?

A Banach algebra that cannot be represented on a Hilbert space

Where is the fallacy in this coupling argument of two Bernoulli variables?

Ring and Subring with different Identities

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