Question

Continuity of functions with multiple variables

score 83 · Answer 1 · 2023-02-20 09:06:59

83

Views

Continuity of functions with multiple variables

Published on 20 Feb 2023 - 9:06

score 78 · Answer 2 · 2023-02-27 16:40:52

78

Views

Homology of the torus

Published on 27 Feb 2023 - 16:40

score 41 · Answer 3 · 2023-03-09 13:40:40

41

Views

Weak convergence on separable and complete product space

Published on 09 Mar 2023 - 13:40

score 72 · Answer 4 · 2026-03-25 23:27:20

72

Views

If the product of closed sets is closed in the product topology shouldn't {(0,0)} be closed in $A^1 \times A^1$ zariski topology.

Published on 25 Mar 2026 - 23:27

score 105 · Answer 5 · 2026-03-25 11:16:24

105

Views

For a closed subset $F ⊂ X × Y$ , the image $π(F )$ need not be closed in Y

Published on 25 Mar 2026 - 11:16

score 59 · Answer 6 · 2023-04-20 18:53:11

59

Views

$X$ is compactly generated (not necessarily Hausdorff) and $Y$ is locally compact, then is $X\times Y$ still compactly generated?

Published on 20 Apr 2023 - 18:53

score 77 · Answer 7 · 2023-04-21 15:46:39

77

Views

Naive question about product topology vs quotient topology

Published on 21 Apr 2023 - 15:46

score 57 · Answer 8 · 2026-03-25 23:33:03

57

Views

$X\times Y$ and the product topology

Published on 25 Mar 2026 - 23:33

score 56 · Answer 9 · 2023-06-05 18:54:58

56

Views

Property of joining of measure preserving systems (or of a measure on a product space).

Published on 05 Jun 2023 - 18:54

score 37 · Answer 10 · 2023-06-26 11:53:03

37

Views

Under what conditions does [for any $x\in X$, $F(x,-): Y\to Z$ is continuous] imply [$F(x,y): X\times Y \to Z$ is continuous]?

Published on 26 Jun 2023 - 11:53

score 89 · Answer 11 · 2023-06-26 17:58:02

89

Views

Show that $\operatorname{int}{(A \times B)} = \operatorname{int}(A) \times \operatorname{int}(B)$

Published on 26 Jun 2023 - 17:58

score 58 · Answer 12 · 2023-06-27 14:40:22

58

Views

Prove explicitly that $\mathbb{R}^2_\text{usual} = (\mathbb{R}_\text{usual})^2$

Published on 27 Jun 2023 - 14:40

score 199 · Answer 13 · 2026-03-25 19:04:51

199

Views

How to prove $\mathbb Z^2 \ast \mathbb Z$ is quasi isometric to $\mathbb Z^2 \ast \mathbb Z^2$?

Published on 25 Mar 2026 - 19:04

score 64 · Answer 14 · 2023-07-13 16:46:28

64

Views

Proof that a mapping into the product space is a topological embedding

Published on 13 Jul 2023 - 16:46

score 45 · Answer 15 · 2023-07-19 15:26:24

45

Views

Right-triangle distance inequality in a product space

Published on 19 Jul 2023 - 15:26

List Question

Continuity of functions with multiple variables

Homology of the torus

Weak convergence on separable and complete product space

If the product of closed sets is closed in the product topology shouldn't {(0,0)} be closed in $A^1 \times A^1$ zariski topology.

For a closed subset $F ⊂ X × Y$ , the image $π(F )$ need not be closed in Y

$X$ is compactly generated (not necessarily Hausdorff) and $Y$ is locally compact, then is $X\times Y$ still compactly generated?

Naive question about product topology vs quotient topology

$X\times Y$ and the product topology

Property of joining of measure preserving systems (or of a measure on a product space).

Under what conditions does [for any $x\in X$, $F(x,-): Y\to Z$ is continuous] imply [$F(x,y): X\times Y \to Z$ is continuous]?

Show that $\operatorname{int}{(A \times B)} = \operatorname{int}(A) \times \operatorname{int}(B)$

Prove explicitly that $\mathbb{R}^2_\text{usual} = (\mathbb{R}_\text{usual})^2$

How to prove $\mathbb Z^2 \ast \mathbb Z$ is quasi isometric to $\mathbb Z^2 \ast \mathbb Z^2$?

Proof that a mapping into the product space is a topological embedding

Right-triangle distance inequality in a product space

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