Question

For nonempty sets $A \subset M, B \subset N$, if $A \times B$ is compact, then $A$ and $B$ are compact.

score 345 · Answer 1 · 2026-04-15 20:31:45

345

Views

For nonempty sets $A \subset M, B \subset N$, if $A \times B$ is compact, then $A$ and $B$ are compact.

Published on 15 Apr 2026 - 20:31

score 39 · Answer 2 · 2026-04-13 07:19:15

39

Views

Question about proof of Heine-Cantor (i.e. compact and continuous implies uniform continuous)

Published on 13 Apr 2026 - 7:19

score 107 · Answer 3 · 2026-04-14 15:23:11

107

Views

Prove that: $\bigcap_{t\in T} \space I_t \neq \varnothing $ for non-disjoint family of intervals from $\mathbb{R}$.

Published on 14 Apr 2026 - 15:23

score 107 · Answer 4 · 2026-04-20 23:24:41

107

Views

Convex sets and semicontinuous functions

Published on 20 Apr 2026 - 23:24

score 612 · Answer 5 · 2026-04-15 10:52:44

612

Views

Arc length of nowhere differentiable arcs.

Published on 15 Apr 2026 - 10:52

score 45 · Answer 6 · 2026-04-16 06:43:38

45

Views

How does this inequality hold? $|d(x,x_0)-d(y,x_0)|\le d(x,y)$

Published on 16 Apr 2026 - 6:43

score 253 · Answer 7 · 2026-04-16 18:30:58

253

Views

Intersection of sequence of compact non empty sets has a similar diameter to the elements in the sequence?

Published on 16 Apr 2026 - 18:30

score 146 · Answer 8 · 2026-04-10 18:20:17

146

Views

Sequence converges iff function is continuous on extension of natural numbers (topology)

Published on 10 Apr 2026 - 18:20

score 75 · Answer 9 · 2026-04-14 03:21:45

75

Views

Defining a set which contains one element per element in another set

Published on 14 Apr 2026 - 3:21

score 184 · Answer 10 · 2026-04-15 07:48:40

184

Views

Convergence of a sequence for the three-point set

Published on 15 Apr 2026 - 7:48

score 118 · Answer 11 · 2026-04-13 15:06:36

118

Views

Proving that a unit disc is open in $\mathbf{R}^2$.

Published on 13 Apr 2026 - 15:06

score 151 · Answer 12 · 2026-04-13 19:52:07

151

Views

Open sets in infinite dimensional spaces

Published on 13 Apr 2026 - 19:52

score 258 · Answer 13 · 2026-04-09 21:51:24

258

Views

Compact refinement of a covering

Published on 09 Apr 2026 - 21:51

score 66 · Answer 14 · 2026-04-11 05:48:14

66

Views

Ultrafilters over product spaces

Published on 11 Apr 2026 - 5:48

score 551 · Answer 15 · 2026-04-15 07:54:47

551

Views

The non-empty intersection of two open discs contains an open disc.

Published on 15 Apr 2026 - 7:54

List Question

For nonempty sets $A \subset M, B \subset N$, if $A \times B$ is compact, then $A$ and $B$ are compact.

Question about proof of Heine-Cantor (i.e. compact and continuous implies uniform continuous)

Prove that: $\bigcap_{t\in T} \space I_t \neq \varnothing $ for non-disjoint family of intervals from $\mathbb{R}$.

Convex sets and semicontinuous functions

Arc length of nowhere differentiable arcs.

How does this inequality hold? $|d(x,x_0)-d(y,x_0)|\le d(x,y)$

Intersection of sequence of compact non empty sets has a similar diameter to the elements in the sequence?

Sequence converges iff function is continuous on extension of natural numbers (topology)

Defining a set which contains one element per element in another set

Convergence of a sequence for the three-point set

Proving that a unit disc is open in $\mathbf{R}^2$.

Open sets in infinite dimensional spaces

Compact refinement of a covering

Ultrafilters over product spaces

The non-empty intersection of two open discs contains an open disc.

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