List questions from examples-counterexamples

Published on 15 Apr 2026 - 13:57

352

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$\sum a_n$ converge but $\sum \sin(a_n)$ diverges?

Published on 13 Apr 2026 - 20:50

45

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Example for a set that is open connected but not path connected in an arbitrary topological space

Published on 10 Apr 2026 - 17:47

57

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Series with elements in $l^{\infty}$ that converge unconditionally but not absolutely

Published on 12 Apr 2026 - 16:16

55

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Is an open covering of $\Bbb Q$ a covering of $\Bbb R$?

Published on 11 Apr 2026 - 22:31

116

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Algebraic vs. continuous representations of topological groups

Published on 10 Apr 2026 - 23:09

356

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Why do we care about Bidual Spaces?

Published on 11 Apr 2026 - 15:19

62

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Show that $(\operatorname{SL}_2\times\operatorname{SL}_2)/N$ is an almost direct product

Published on 12 Apr 2026 - 1:09

272

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A continuous bounded variation function in $[0,1]$ that is absolutely continuous in $(a,1]$, but is not in $[0,1]$

Published on 12 Apr 2026 - 21:14

506

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Examples of Finite-Duration solutions to Autonomous Ordinary Differential Equations ODEs?

Published on 25 Apr 2026 - 15:09

92

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Confusion about an answer - why does this element have to be unique?

Published on 17 Apr 2026 - 5:18

45

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proof/counterexample about local extrema of composite function

Published on 08 Apr 2026 - 21:06

167

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Elementary Applications of Algebraic Geometry

Published on 13 Apr 2026 - 14:31

144

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True or False: If a series converges, then so does the series formed by the product of each member of it's power set

Published on 16 Apr 2026 - 12:14

41

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Gelfand's corrolaries counterexample?

Published on 15 Apr 2026 - 5:31

List Question

Graph where edges have group structure

$\sum a_n$ converge but $\sum \sin(a_n)$ diverges?

Example for a set that is open connected but not path connected in an arbitrary topological space

Series with elements in $l^{\infty}$ that converge unconditionally but not absolutely

Is an open covering of $\Bbb Q$ a covering of $\Bbb R$?

Algebraic vs. continuous representations of topological groups

Why do we care about Bidual Spaces?

Show that $(\operatorname{SL}_2\times\operatorname{SL}_2)/N$ is an almost direct product

A continuous bounded variation function in $[0,1]$ that is absolutely continuous in $(a,1]$, but is not in $[0,1]$

Examples of Finite-Duration solutions to Autonomous Ordinary Differential Equations ODEs?

Confusion about an answer - why does this element have to be unique?

proof/counterexample about local extrema of composite function

Elementary Applications of Algebraic Geometry

True or False: If a series converges, then so does the series formed by the product of each member of it's power set

Gelfand's corrolaries counterexample?

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