Proof verification that $\overline{\mathbb{R}^{\infty}} = \mathbb{R^\omega}$ and $\overline{\mathbb{R}^{\infty}} = \mathbb{R^\infty}$ in prod/box top.

score 412 · Answer 7 · 2026-04-16 23:14:25

412

Views

Construct homotopy from $(\alpha \cdot \beta) \cdot \gamma$ to $\alpha \cdot (\beta \cdot \gamma)$ explicitly

Published on 16 Apr 2026 - 23:14

score 463 · Answer 8 · 2026-04-11 13:27:29

463

Views

Show the closure of a subset of a complete metric space is compact.

Published on 11 Apr 2026 - 13:27

score 98 · Answer 9 · 2026-05-14 14:25:12

98

Views

Possible use of choice in proving "Compactness implies limit point compactness"

Published on 14 May 2026 - 14:25

score 32 · Answer 10 · 2026-04-13 15:55:11

32

Views

Interior of a subset of $\mathbb{R}^3$ where $(x,y)\in\mathbb{Q}^2$

Published on 13 Apr 2026 - 15:55

score 31 · Answer 11 · 2026-04-15 07:47:21

31

Views

Construction of a function from $\mathbb R^{\mathbb R^2}\to \mathbb R^\Gamma $ where $\Gamma =\mathbb R^2/_\sim$.

Published on 15 Apr 2026 - 7:47

score 594 · Answer 12 · 2026-04-16 17:51:12

594

Views

If $X$ is a real normed linear space, then $B(0,r)=r B(0,1)$

Published on 16 Apr 2026 - 17:51

score 67 · Answer 13 · 2026-04-15 18:15:06

67

Views

Joint essential range of $\varphi\in L^\infty(X,\mu)^d$.

Published on 15 Apr 2026 - 18:15

score 76 · Answer 14 · 2026-04-12 21:40:21

76

Views

When are two quotient Topologies homeomorphic

Published on 12 Apr 2026 - 21:40

score 51 · Answer 15 · 2026-04-11 15:42:28

51

Views

Language/notation abuse when considering an open set of the product topology

Published on 11 Apr 2026 - 15:42

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Proof verification that $\overline{\mathbb{R}^{\infty}} = \mathbb{R^\omega}$ and $\overline{\mathbb{R}^{\infty}} = \mathbb{R^\infty}$ in prod/box top.

Construct homotopy from $(\alpha \cdot \beta) \cdot \gamma$ to $\alpha \cdot (\beta \cdot \gamma)$ explicitly

Show the closure of a subset of a complete metric space is compact.

Possible use of choice in proving "Compactness implies limit point compactness"

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Construction of a function from $\mathbb R^{\mathbb R^2}\to \mathbb R^\Gamma $ where $\Gamma =\mathbb R^2/_\sim$.

If $X$ is a real normed linear space, then $B(0,r)=r B(0,1)$

Joint essential range of $\varphi\in L^\infty(X,\mu)^d$.

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Language/notation abuse when considering an open set of the product topology

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