Question

Show that the union of complete sets is not necessarily complete

score 808 · Answer 1 · 2026-03-25 13:33:19

808

Views

Show that the union of complete sets is not necessarily complete

Published on 25 Mar 2026 - 13:33

score 538 · Answer 2 · 2026-03-31 22:08:27

538

Views

How to proof the Interior and clousure of subset of R^3

Published on 31 Mar 2026 - 22:08

score 86 · Answer 3 · 2026-03-31 22:10:52

86

Views

Showing $\rho$ is a metric inside a metric space $(X, d)$

Published on 31 Mar 2026 - 22:10

score 80 · Answer 4 · 2026-03-31 22:03:59

80

Views

Prove each subset using isolated points.

Published on 31 Mar 2026 - 22:03

score 962 · Answer 5 · 2026-03-25 23:11:03

962

Views

$X$ a compact Hausdorff space and a sequence $A_1 \supset A_2 \supset \dots$ of closed connected subsets. Show that $\bigcap A_n$ is also connected.

Published on 25 Mar 2026 - 23:11

score 68 · Answer 6 · 2018-05-11 12:22:28

68

Views

Existence of a special set in $\mathbb{R}^2$

Published on 11 May 2018 - 12:22

score 310 · Answer 7 · 2018-05-11 12:59:36

310

Views

Dense set in a compact subset, then dense in the whole space?

Published on 11 May 2018 - 12:59

score 183 · Answer 8 · 2026-03-30 17:37:04

183

Views

Orientable Double Cover of $\mathbb{R}\mathbb{P}^2 \times \mathbb{R}\mathbb{P}^2$

Published on 30 Mar 2026 - 17:37

score 124 · Answer 9 · 2026-03-28 04:53:15

124

Views

$\prod X_{a\in A} $ with the box topology is compact, show that $X_a$ is compact for every $a\in A$

Published on 28 Mar 2026 - 4:53

score 72 · Answer 10 · 2018-05-11 13:50:53

72

Views

What are some of the nontrivial way to define open set on natural numbers?

Published on 11 May 2018 - 13:50

score 392 · Answer 11 · 2026-03-25 22:23:53

392

Views

Small oscillation of spherical pendulum

Published on 25 Mar 2026 - 22:23

score 340 · Answer 12 · 2018-05-11 15:17:56

340

Views

Continuous map from open unit interval to the square such that the range and its complement are both dense

Published on 11 May 2018 - 15:17

score 163 · Answer 13 · 2026-04-01 18:32:47

163

Views

Prove that if $W$ is an open subset of $Y$ then the set $\{x\in X: f(x)\in W\}$ is an open subset of $X$.

Published on 01 Apr 2026 - 18:32

score 178 · Answer 14 · 2026-03-24 23:51:12

178

Views

A set with Borel preimage

Published on 24 Mar 2026 - 23:51

score 139 · Answer 15 · 2026-03-25 06:06:33

139

Views

Existence of open set in $R^2$ such that all open sets in $R$ are contained among its vertical sections

Published on 25 Mar 2026 - 6:06

List Question

Show that the union of complete sets is not necessarily complete

How to proof the Interior and clousure of subset of R^3

Showing $\rho$ is a metric inside a metric space $(X, d)$

Prove each subset using isolated points.

$X$ a compact Hausdorff space and a sequence $A_1 \supset A_2 \supset \dots$ of closed connected subsets. Show that $\bigcap A_n$ is also connected.

Existence of a special set in $\mathbb{R}^2$

Dense set in a compact subset, then dense in the whole space?

Orientable Double Cover of $\mathbb{R}\mathbb{P}^2 \times \mathbb{R}\mathbb{P}^2$

$\prod X_{a\in A} $ with the box topology is compact, show that $X_a$ is compact for every $a\in A$

What are some of the nontrivial way to define open set on natural numbers?

Small oscillation of spherical pendulum

Continuous map from open unit interval to the square such that the range and its complement are both dense

Prove that if $W$ is an open subset of $Y$ then the set $\{x\in X: f(x)\in W\}$ is an open subset of $X$.

A set with Borel preimage

Existence of open set in $R^2$ such that all open sets in $R$ are contained among its vertical sections

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