Question

My attempt of constructing a bijection between $(0,1]$ and $(0,1)$

score 73 · Answer 1 · 2026-04-13 15:31:25

73

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My attempt of constructing a bijection between $(0,1]$ and $(0,1)$

Published on 13 Apr 2026 - 15:31

score 108 · Answer 2 · 2026-04-11 09:20:13

108

Views

Induced orientations on manifolds - explanation and example

Published on 11 Apr 2026 - 9:20

score 56 · Answer 3 · 2026-04-14 13:05:02

56

Views

Show that $\bigcup_{t\in I}U_t\times\{t\}$ could be not open although $I$ is open and $U_t$ is open for each $t\in I$.

Published on 14 Apr 2026 - 13:05

score 103 · Answer 4 · 2026-04-09 15:26:09

103

Views

An example of a ring which is very close to division ring but not a division ring.

Published on 09 Apr 2026 - 15:26

score 168 · Answer 5 · 2026-04-15 17:36:28

168

Views

$(X,\mathcal{S})$ measure space, $f:X\to [-\infty,\infty], f^{-1}((a,\infty))\in\mathcal{S}$ for all $a\in\mathbb{R}$ does not imply $f$ is measurable

Published on 15 Apr 2026 - 17:36

score 457 · Answer 6 · 2026-04-16 10:23:49

457

Views

Monoid where every element has a one-sided inverse is a group.

Published on 16 Apr 2026 - 10:23

score 327 · Answer 7 · 2026-04-17 10:59:31

327

Views

Is it true that $\frac{a_1^2}{a_2}+\frac{a_2^2}{a_3}+\cdots+\frac{a_n^2}{a_1}\geq\sqrt{n(a_1^2+a_2^2+\cdots+a_n^2)}$ for positive real $a_i$?

Published on 17 Apr 2026 - 10:59

score 48 · Answer 8 · 2026-04-11 19:21:14

48

Views

Are there subsets of every size in a union-closed family?

Published on 11 Apr 2026 - 19:21

score 64 · Answer 9 · 2026-04-10 20:04:40

64

Views

Example of situation in which adding inequations introduces an infinity of extraneous solutions and only one true solution.

Published on 10 Apr 2026 - 20:04

score 61 · Answer 10 · 2026-04-17 19:25:50

61

Views

If $f(x,t)$ is of class $C^1$ then does $f_n(x):=\frac{f(x,t_n)-f(x,t_0)}{t_n-t_0}$ uniformly converge to $\frac{\partial f}{\partial t}(x,t_0)$?

Published on 17 Apr 2026 - 19:25

score 290 · Answer 11 · 2026-04-12 02:05:45

290

Views

For an integral domain $A$, if $\#{\rm Spec}\ A=\infty$, then $\bigcap_{\mathfrak{p}\neq (0)}\mathfrak{p}=(0)$?

Published on 12 Apr 2026 - 2:05

score 162 · Answer 12 · 2026-04-14 14:18:27

162

Views

a counter-example for the existence of the direct limits in $\mathbf{Ban}$

Published on 14 Apr 2026 - 14:18

score 57 · Answer 13 · 2026-04-12 20:58:04

57

Views

In search for easy counterexample of $L^2$ ineq. - if it exists

Published on 12 Apr 2026 - 20:58

score 78 · Answer 14 · 2026-04-10 00:12:00

78

Views

Questions about the definition of smooth paths in complex anlaysis

Published on 10 Apr 2026 - 0:12

score 323 · Answer 15 · 2026-04-11 15:12:31

323

Views

Example of a map of coverings which is not a covering map, if the base space is not locally path-connected

Published on 11 Apr 2026 - 15:12

List Question

My attempt of constructing a bijection between $(0,1]$ and $(0,1)$

Induced orientations on manifolds - explanation and example

Show that $\bigcup_{t\in I}U_t\times\{t\}$ could be not open although $I$ is open and $U_t$ is open for each $t\in I$.

An example of a ring which is very close to division ring but not a division ring.

$(X,\mathcal{S})$ measure space, $f:X\to [-\infty,\infty], f^{-1}((a,\infty))\in\mathcal{S}$ for all $a\in\mathbb{R}$ does not imply $f$ is measurable

Monoid where every element has a one-sided inverse is a group.

Is it true that $\frac{a_1^2}{a_2}+\frac{a_2^2}{a_3}+\cdots+\frac{a_n^2}{a_1}\geq\sqrt{n(a_1^2+a_2^2+\cdots+a_n^2)}$ for positive real $a_i$?

Are there subsets of every size in a union-closed family?

Example of situation in which adding inequations introduces an infinity of extraneous solutions and only one true solution.

If $f(x,t)$ is of class $C^1$ then does $f_n(x):=\frac{f(x,t_n)-f(x,t_0)}{t_n-t_0}$ uniformly converge to $\frac{\partial f}{\partial t}(x,t_0)$?

For an integral domain $A$, if $\#{\rm Spec}\ A=\infty$, then $\bigcap_{\mathfrak{p}\neq (0)}\mathfrak{p}=(0)$?

a counter-example for the existence of the direct limits in $\mathbf{Ban}$

In search for easy counterexample of $L^2$ ineq. - if it exists

Questions about the definition of smooth paths in complex anlaysis

Example of a map of coverings which is not a covering map, if the base space is not locally path-connected

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