Question

If $B = B_1 \cup B_2$ where B is open and $B_1$ and $B_2$ are disjoint, then is it true that $B_1$ and $B_2$ are both open?

score 174 · Answer 1 · 2016-08-05 01:11:23

174

Views

If $B = B_1 \cup B_2$ where B is open and $B_1$ and $B_2$ are disjoint, then is it true that $B_1$ and $B_2$ are both open?

Published on 05 Aug 2016 - 1:11

score 536 · Answer 2 · 2016-08-06 20:38:28

536

Views

Is there a simple geometric example of unequal left and right cosets?

Published on 06 Aug 2016 - 20:38

score 58 · Answer 3 · 2016-08-07 11:58:01

58

Views

Union of domain of semidifferentials

Published on 07 Aug 2016 - 11:58

score 139 · Answer 4 · 2016-08-07 23:37:53

139

Views

Example of $L^p$ function which does not have much Lebesgue points

Published on 07 Aug 2016 - 23:37

score 12k · Answer 5 · 2026-03-29 03:03:52

12k

Views

Examples of problems that are easier in the infinite case than in the finite case.

Published on 29 Mar 2026 - 3:03

score 314 · Answer 6 · 2016-08-09 08:35:04

314

Views

Example of a ring having an ideal that does not contain a product of finitely many prime ideals

Published on 09 Aug 2016 - 8:35

score 30 · Answer 7 · 2026-03-25 11:03:11

30

Views

Verification: (Stationary points of) real-valued submersion on differentiable manifolds

Published on 25 Mar 2026 - 11:03

score 2k · Answer 8 · 2016-08-13 23:42:50

2k

Views

"If $f$ is a linear function of the form $f(x)=mx+b$, then $f(u+v)=f(u)+f(v).$" True or false?

Published on 13 Aug 2016 - 23:42

score 50 · Answer 9 · 2016-08-14 06:49:56

50

Views

For suitable $a,b$, is it true that $(a+b) \nmid a^{m}$ for all $m \geq 2$?

Published on 14 Aug 2016 - 6:49

score 705 · Answer 10 · 2016-08-16 12:03:15

705

Views

Can the long line be embedded in euclidean space?

Published on 16 Aug 2016 - 12:03

score 501 · Answer 11 · 2016-08-16 12:41:12

501

Views

Endofunctors of $\mathbf{Set}$ that don't preserve monomorphisms

Published on 16 Aug 2016 - 12:41

score 317 · Answer 12 · 2016-08-16 23:07:58

317

Views

Example that Schwarz's theorem does not hold

Published on 16 Aug 2016 - 23:07

score 208 · Answer 13 · 2026-04-02 06:08:46

208

Views

Countable sum of closed totally disconnected spaces

Published on 02 Apr 2026 - 6:08

score 255 · Answer 14 · 2026-03-28 13:21:23

255

Views

Torsion in homology of a subset $E \subset \Bbb R^n$ with $n≤2$

Published on 28 Mar 2026 - 13:21

score 166 · Answer 15 · 2016-08-19 20:34:01

166

Views

A calculus conjecture about sum and derivative

Published on 19 Aug 2016 - 20:34

List Question

If $B = B_1 \cup B_2$ where B is open and $B_1$ and $B_2$ are disjoint, then is it true that $B_1$ and $B_2$ are both open?

Is there a simple geometric example of unequal left and right cosets?

Union of domain of semidifferentials

Example of $L^p$ function which does not have much Lebesgue points

Examples of problems that are easier in the infinite case than in the finite case.

Example of a ring having an ideal that does not contain a product of finitely many prime ideals

Verification: (Stationary points of) real-valued submersion on differentiable manifolds

"If $f$ is a linear function of the form $f(x)=mx+b$, then $f(u+v)=f(u)+f(v).$" True or false?

For suitable $a,b$, is it true that $(a+b) \nmid a^{m}$ for all $m \geq 2$?

Can the long line be embedded in euclidean space?

Endofunctors of $\mathbf{Set}$ that don't preserve monomorphisms

Example that Schwarz's theorem does not hold

Countable sum of closed totally disconnected spaces

Torsion in homology of a subset $E \subset \Bbb R^n$ with $n≤2$

A calculus conjecture about sum and derivative

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