Question

Examples of topological spaces with canonical bases with the following property (redivisibility)

score 57 · Answer 1 · 2026-04-15 04:11:56

57

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Examples of topological spaces with canonical bases with the following property (redivisibility)

Published on 15 Apr 2026 - 4:11

score 35 · Answer 2 · 2026-04-10 01:56:05

35

Views

Properties of a set $A\subseteq\Bbb R^n$ for which the statement $(\partial A)'=\partial(A')$ doesn't hold.

Published on 10 Apr 2026 - 1:56

score 1.5k · Answer 3 · 2026-04-11 15:12:47

1.5k

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About $\rho(x, y)= \begin{cases}\mathrm{d}(x, y) & \mathrm{d}(x, y)<1 \\ 1 & \mathrm{~d}(x, y) \geq 1\end{cases}$ in a metric space

Published on 11 Apr 2026 - 15:12

score 140 · Answer 4 · 2026-04-16 13:25:24

140

Views

Is true that $\bigcup\Big(\bigcup( A\times B)\Big)=A\cup B$ for any pair of sets $A$ and $B$?

Published on 16 Apr 2026 - 13:25

score 87 · Answer 5 · 2026-04-14 20:14:33

87

Views

Clarify if $A⊆\mathcal R^{-1}\big[\mathcal R[A]\big]$ and if $\mathcal R\big[\mathcal R^{-1}[B]\big]=B\cap\text{ran }\mathcal R$ for any relation

Published on 14 Apr 2026 - 20:14

score 69 · Answer 6 · 2026-04-10 18:10:17

69

Views

Instance of a non-compact and non-euclidean complex manifolds

Published on 10 Apr 2026 - 18:10

score 167 · Answer 7 · 2026-04-17 01:10:01

167

Views

Bounded convex sets $A,B\subseteq\Bbb R^n,n\ge 2$ with a common point, but disjoint boundaries

Published on 17 Apr 2026 - 1:10

score 95 · Answer 8 · 2026-04-17 06:11:54

95

Views

Construction of $g:\mathbb{N}\rightarrow\mathbb{N}$ surjective, such that $g^{-1}(n)=\infty,\;\forall n\in\mathbb{N}$

Published on 17 Apr 2026 - 6:11

score 85 · Answer 9 · 2026-04-14 18:42:11

85

Views

Example of non-integral-domain such that all localizations at primes are integral domains.

Published on 14 Apr 2026 - 18:42

score 334 · Answer 10 · 2026-04-14 14:56:02

334

Views

Removal of an arbitrary point of the boundary of a closed and connected $A\subseteq\Bbb R^2$ so the new set remains connected

Published on 14 Apr 2026 - 14:56

score 109 · Answer 11 · 2026-04-14 17:06:05

109

Views

Bump functions whose derivatives $f^{(n)}(x)$ converge to $0$ uniformly as $n\to\infty$

Published on 14 Apr 2026 - 17:06

score 196 · Answer 12 · 2026-04-18 20:24:52

196

Views

If $φ:I→J$ is a homeomorphism then $f_n→f$ implies that $(f_n∘φ) →(f∘φ)$ with respect the uniform, pointwise and $L_2$ topology respectively?

Published on 18 Apr 2026 - 20:24

score 40 · Answer 13 · 2026-03-25 20:42:08

40

Views

Examples of incomplete normed spaces of continuous linear maps between two normed spaces

Published on 25 Mar 2026 - 20:42

score 384 · Answer 14 · 2026-04-13 14:18:33

384

Views

Determining if two graphs are homeomorphic by smoothing?

Published on 13 Apr 2026 - 14:18

score 76 · Answer 15 · 2026-04-14 22:14:17

76

Views

A counter example for $\Gamma\vDash_{v}B\Longleftrightarrow\Gamma\cup\{\neg B\}$ isn't satisfiable by a model

Published on 14 Apr 2026 - 22:14

List Question

Examples of topological spaces with canonical bases with the following property (redivisibility)

Properties of a set $A\subseteq\Bbb R^n$ for which the statement $(\partial A)'=\partial(A')$ doesn't hold.

About $\rho(x, y)= \begin{cases}\mathrm{d}(x, y) & \mathrm{d}(x, y)<1 \\ 1 & \mathrm{~d}(x, y) \geq 1\end{cases}$ in a metric space

Is true that $\bigcup\Big(\bigcup( A\times B)\Big)=A\cup B$ for any pair of sets $A$ and $B$?

Clarify if $A⊆\mathcal R^{-1}\big[\mathcal R[A]\big]$ and if $\mathcal R\big[\mathcal R^{-1}[B]\big]=B\cap\text{ran }\mathcal R$ for any relation

Instance of a non-compact and non-euclidean complex manifolds

Bounded convex sets $A,B\subseteq\Bbb R^n,n\ge 2$ with a common point, but disjoint boundaries

Construction of $g:\mathbb{N}\rightarrow\mathbb{N}$ surjective, such that $g^{-1}(n)=\infty,\;\forall n\in\mathbb{N}$

Example of non-integral-domain such that all localizations at primes are integral domains.

Removal of an arbitrary point of the boundary of a closed and connected $A\subseteq\Bbb R^2$ so the new set remains connected

Bump functions whose derivatives $f^{(n)}(x)$ converge to $0$ uniformly as $n\to\infty$

If $φ:I→J$ is a homeomorphism then $f_n→f$ implies that $(f_n∘φ) →(f∘φ)$ with respect the uniform, pointwise and $L_2$ topology respectively?

Examples of incomplete normed spaces of continuous linear maps between two normed spaces

Determining if two graphs are homeomorphic by smoothing?

A counter example for $\Gamma\vDash_{v}B\Longleftrightarrow\Gamma\cup\{\neg B\}$ isn't satisfiable by a model

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