Question

How do I prove the $f:X\to I$ by $f(x)=\min\{f_i(x_{\beta_i}):i=1,2,...,n\}$ is continuous.

score 38 · Answer 1 · 2026-04-14 15:04:50

38

Views

How do I prove the $f:X\to I$ by $f(x)=\min\{f_i(x_{\beta_i}):i=1,2,...,n\}$ is continuous.

Published on 14 Apr 2026 - 15:04

score 175 · Answer 2 · 2026-04-14 03:59:19

175

Views

Is the subspace topology of the product topology the initial topology with respect to the restrictions of the projection maps?

Published on 14 Apr 2026 - 3:59

score 108 · Answer 3 · 2026-04-13 21:19:32

108

Views

Every bounded net in a dual space has a cluster point?

Published on 13 Apr 2026 - 21:19

score 666 · Answer 4 · 2026-04-12 14:15:05

666

Views

Proof Verification: Show that if Y is compact, then the projection is a closed map

Published on 12 Apr 2026 - 14:15

score 129 · Answer 5 · 2026-05-10 17:28:44

129

Views

Cellularity of product space

Published on 10 May 2026 - 17:28

score 262 · Answer 6 · 2026-05-10 16:34:31

262

Views

$+:X\times X\to X,(x,y)\mapsto +(x,y)=x+y$ and $\cdot:\Bbb{R}\times X\to X,(\lambda,x)\mapsto \cdot(\lambda,y)=\lambda\cdot x$ are weakly continuous

Published on 10 May 2026 - 16:34

score 283 · Answer 7 · 2026-04-13 17:41:15

283

Views

When is the product of closed sets closed in the product topology?

Published on 13 Apr 2026 - 17:41

score 67 · Answer 8 · 2026-04-10 11:35:13

67

Views

Does a sequentially continuous function take its supremum on compacts?

Published on 10 Apr 2026 - 11:35

score 51 · Answer 9 · 2026-04-12 22:48:51

51

Views

Continuity of countable projection from non-first countable topological space

Published on 12 Apr 2026 - 22:48

score 132 · Answer 10 · 2026-04-15 00:23:40

132

Views

Show $g$ integrable over [0, 1] if $g(x) - g(y)$ is Lebesgue integrable over $[0, 1] \times [0, 1]$

Published on 15 Apr 2026 - 0:23

score 96 · Answer 11 · 2026-04-11 04:08:17

96

Views

Product topology. Clarification needed

Published on 11 Apr 2026 - 4:08

score 198 · Answer 12 · 2026-04-13 11:41:35

198

Views

Product of two sequential spaces is not sequential

Published on 13 Apr 2026 - 11:41

score 214 · Answer 13 · 2026-04-11 12:55:34

214

Views

Assume that Y is compact. Prove that f is continuous.

Published on 11 Apr 2026 - 12:55

score 62 · Answer 14 · 2026-05-10 14:49:42

62

Views

Topology of the automorphic quotient

Published on 10 May 2026 - 14:49

score 72 · Answer 15 · 2026-04-14 16:50:04

72

Views

What's the correct version of this "product rule" is topology?

Published on 14 Apr 2026 - 16:50

List Question

How do I prove the $f:X\to I$ by $f(x)=\min\{f_i(x_{\beta_i}):i=1,2,...,n\}$ is continuous.

Is the subspace topology of the product topology the initial topology with respect to the restrictions of the projection maps?

Every bounded net in a dual space has a cluster point?

Proof Verification: Show that if Y is compact, then the projection is a closed map

Cellularity of product space

$+:X\times X\to X,(x,y)\mapsto +(x,y)=x+y$ and $\cdot:\Bbb{R}\times X\to X,(\lambda,x)\mapsto \cdot(\lambda,y)=\lambda\cdot x$ are weakly continuous

When is the product of closed sets closed in the product topology?

Does a sequentially continuous function take its supremum on compacts?

Continuity of countable projection from non-first countable topological space

Show $g$ integrable over [0, 1] if $g(x) - g(y)$ is Lebesgue integrable over $[0, 1] \times [0, 1]$

Product topology. Clarification needed

Product of two sequential spaces is not sequential

Assume that Y is compact. Prove that f is continuous.

Topology of the automorphic quotient

What's the correct version of this "product rule" is topology?

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