Question

How can we show that $C_c^\infty(\mathbb R)$ strongly separates points?

score 149 · Answer 1 · 2026-04-12 16:21:06

149

Views

How can we show that $C_c^\infty(\mathbb R)$ strongly separates points?

Published on 12 Apr 2026 - 16:21

score 39 · Answer 2 · 2026-04-15 03:42:13

39

Views

Recipe for embedding $m$-fold product $X_m := S^1 \ \times ... \times \ S^1$ onto a bounded subset of $\mathbb{R}^{m+1}$

Published on 15 Apr 2026 - 3:42

score 115 · Answer 3 · 2026-04-16 01:58:13

115

Views

Showing the image of a surjective map from a regular topological space is also regular

Published on 16 Apr 2026 - 1:58

score 643 · Answer 4 · 2026-04-16 11:02:21

643

Views

Proving $[0,1]\cap\mathbb{Q}$ is not compact in $\mathbb{Q}$

Published on 16 Apr 2026 - 11:02

score 896 · Answer 5 · 2026-04-09 12:19:19

896

Views

Proof verification: All metric spaces gave the "Hausdorff property".

Published on 09 Apr 2026 - 12:19

score 49 · Answer 6 · 2026-04-14 02:52:07

49

Views

Show that a disjoint family $(I_\lambda)_{\lambda \in \Lambda}$ of not degenerate intervals of $\Bbb{R}$ is at most denumerable

Published on 14 Apr 2026 - 2:52

score 89 · Answer 7 · 2026-03-26 01:06:17

89

Views

Can a noncompact metric space have a maximal metrizable Hausdorff compactification?

Published on 26 Mar 2026 - 1:06

score 1.3k · Answer 8 · 2026-04-16 21:59:56

1.3k

Views

Determine whether $S=\{x,y\in \mathbb{R}^2 : x^2-y^2=1\}$ is disconnected or connected.

Published on 16 Apr 2026 - 21:59

score 121 · Answer 9 · 2026-04-17 07:36:57

121

Views

Path from an invertible matrix $A$ to a diagonal matrix $E=(e_{ij})$ with $e_{11}=\mbox{sgn}(\det (A))$

Published on 17 Apr 2026 - 7:36

score 134 · Answer 10 · 2026-04-12 01:58:40

134

Views

Is the set $\{2,3,5\}$ connected?

Published on 12 Apr 2026 - 1:58

score 43 · Answer 11 · 2026-04-09 19:12:36

43

Views

Metric on compact set with one point less

Published on 09 Apr 2026 - 19:12

score 51 · Answer 12 · 2026-04-17 14:42:14

51

Views

Radius of an Open Ball inside the Intersection of an Open, Dense Subset and the Ball Around a Point in the Set

Published on 17 Apr 2026 - 14:42

score 170 · Answer 13 · 2026-04-13 04:32:45

170

Views

linear isometric embedding from $(\mathbb{R}^2, \| \|_2)$ to $(l^1, \| \|_1)$

Published on 13 Apr 2026 - 4:32

score 278 · Answer 14 · 2026-04-16 12:17:56

278

Views

Is $\Bbb Q / \Bbb Z$ discrete?

Published on 16 Apr 2026 - 12:17

score 167 · Answer 15 · 2026-04-14 21:57:26

167

Views

Prove that there is no finite subcover

Published on 14 Apr 2026 - 21:57

List Question

How can we show that $C_c^\infty(\mathbb R)$ strongly separates points?

Recipe for embedding $m$-fold product $X_m := S^1 \ \times ... \times \ S^1$ onto a bounded subset of $\mathbb{R}^{m+1}$

Showing the image of a surjective map from a regular topological space is also regular

Proving $[0,1]\cap\mathbb{Q}$ is not compact in $\mathbb{Q}$

Proof verification: All metric spaces gave the "Hausdorff property".

Show that a disjoint family $(I_\lambda)_{\lambda \in \Lambda}$ of not degenerate intervals of $\Bbb{R}$ is at most denumerable

Can a noncompact metric space have a maximal metrizable Hausdorff compactification?

Determine whether $S=\{x,y\in \mathbb{R}^2 : x^2-y^2=1\}$ is disconnected or connected.

Path from an invertible matrix $A$ to a diagonal matrix $E=(e_{ij})$ with $e_{11}=\mbox{sgn}(\det (A))$

Is the set $\{2,3,5\}$ connected?

Metric on compact set with one point less

Radius of an Open Ball inside the Intersection of an Open, Dense Subset and the Ball Around a Point in the Set

linear isometric embedding from $(\mathbb{R}^2, \| \|_2)$ to $(l^1, \| \|_1)$

Is $\Bbb Q / \Bbb Z$ discrete?

Prove that there is no finite subcover

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