List questions from examples-counterexamples

Published on 09 Apr 2026 - 15:19

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Intersection of clopen sets that contain x is the connected component of x (if X is compact)

Published on 16 Sep 2015 - 15:08

595

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Is there a simple closed curve which is not rectifiable?

Published on 09 Apr 2026 - 14:06

1.6k

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Prove or give Counterexample: Is this a Basis.

Published on 18 Sep 2015 - 8:52

703

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how to prove that $abc$ and $cba$ do not necessarily have the same order?

Published on 19 Sep 2015 - 0:10

100

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A generalized Alexandroff space that is not an Alexandroff space

Published on 19 Sep 2015 - 13:41

49

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Give a counterexample to $\bigcup\limits_{t \in T} (A_t \cap B_t)= \bigcup\limits_{t \in T} A_t \cap \bigcup\limits_{t \in T} B_t$

Published on 19 Sep 2015 - 15:50

35

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When is $\Pr(U\leq v|V=v)$ not an increasing function of $v$?

Published on 19 Sep 2015 - 19:09

114

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Functions such that $f(g(x)) = x$ but $g(f(x)) \neq x $

Published on 20 Sep 2015 - 6:57

2.3k

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Example where $x^2 = e$ has more than two solutions in a group

Published on 20 Sep 2015 - 12:42

1.2k

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Non-constant continuous function having uncountably many zeros?

Published on 21 Sep 2015 - 16:00

250

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Good example showing why limits must exist in limit product rule

Published on 09 Apr 2026 - 2:22

2k

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Example of a group action G on a vector space V that fails to be linear (i.e. fails to be a linear representation).

Published on 02 Apr 2026 - 12:32

408

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non-trivial non-repetitive aperiodic tiling of the plane

Published on 27 Mar 2026 - 2:37

153

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Example of a function s.t. $f\in C^{1}$ and $f'\notin L^{1}$?

Published on 30 Mar 2026 - 13:39

List Question

Reflexive but not separable space

Intersection of clopen sets that contain x is the connected component of x (if X is compact)

Is there a simple closed curve which is not rectifiable?

Prove or give Counterexample: Is this a Basis.

how to prove that $abc$ and $cba$ do not necessarily have the same order?

A generalized Alexandroff space that is not an Alexandroff space

Give a counterexample to $\bigcup\limits_{t \in T} (A_t \cap B_t)= \bigcup\limits_{t \in T} A_t \cap \bigcup\limits_{t \in T} B_t$

When is $\Pr(U\leq v|V=v)$ not an increasing function of $v$?

Functions such that $f(g(x)) = x$ but $g(f(x)) \neq x $

Example where $x^2 = e$ has more than two solutions in a group

Non-constant continuous function having uncountably many zeros?

Good example showing why limits must exist in limit product rule

Example of a group action G on a vector space V that fails to be linear (i.e. fails to be a linear representation).

non-trivial non-repetitive aperiodic tiling of the plane

Example of a function s.t. $f\in C^{1}$ and $f'\notin L^{1}$?

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