Question

prove that $\mathbb{Q}$ can not be $G_{\delta}$ set in $\mathbb{R}$.

score 95 · Answer 1 · 2026-04-16 02:44:21

95

Views

prove that $\mathbb{Q}$ can not be $G_{\delta}$ set in $\mathbb{R}$.

Published on 16 Apr 2026 - 2:44

score 290 · Answer 2 · 2026-05-04 20:41:43

290

Views

If $F \subset \mathbb{R}$ and bounded, then sup $F \in \bar{F}$

Published on 04 May 2026 - 20:41

score 271 · Answer 3 · 2026-04-14 11:29:23

271

Views

Show that Hill's Equation $u'' + a(t)u=0$ if $a(t)<0$ for all $t$ then $u\to\infty$ as $t\to\infty$

Published on 14 Apr 2026 - 11:29

score 19 · Answer 4 · 2026-05-03 10:31:43

19

Views

Showing that $\Psi: l_1 \rightarrow l_1$ such that $\Psi (u)=v$ where $v_n = \sum^{n}_{p=1}u_pu_{n-p}$ is differentiable.

Published on 03 May 2026 - 10:31

score 765 · Answer 5 · 2026-04-29 12:54:25

765

Views

Is the sum of a Darboux function and a continuous function Darboux?

Published on 29 Apr 2026 - 12:54

score 98 · Answer 6 · 2026-04-16 08:50:36

98

Views

Generalization of convexity

Published on 16 Apr 2026 - 8:50

score 119 · Answer 7 · 2026-04-29 12:46:55

119

Views

There is no smooth diffeomorphism $f:\mathbb R^3 \setminus [-\frac{1}{2}, \frac{1}{2}]^3 \to \mathbb R^3$

Published on 29 Apr 2026 - 12:46

score 136 · Answer 8 · 2026-04-14 22:49:20

136

Views

Sum of series $\sum_1 \frac{\cos(x)^{n-1}}{n!}$

Published on 14 Apr 2026 - 22:49

score 79 · Answer 9 · 2026-04-29 13:04:44

79

Views

Bound a natural by two consecutive powers

Published on 29 Apr 2026 - 13:04

score 896 · Answer 10 · 2026-04-10 23:59:04

896

Views

If a normed space is finite dimensional, the unit sphere is compact

Published on 10 Apr 2026 - 23:59

score 2.5k · Answer 11 · 2026-04-15 15:20:30

2.5k

Views

Uniform convergence of alternating series

Published on 15 Apr 2026 - 15:20

score 1.4k · Answer 12 · 2026-04-21 11:06:16

1.4k

Views

Why does the commutative property of addition not hold for conditionally convergent series?

Published on 21 Apr 2026 - 11:06

score 212 · Answer 13 · 2026-04-11 02:02:11

212

Views

Describing continuous functions

Published on 11 Apr 2026 - 2:02

score 39 · Answer 14 · 2026-04-16 04:33:31

If ${ X_n }$ is a sequence of real numbers and E = set of all numbers z s.t. $\exists$ a subsequence ${ X_{n_k} }$ convergent to z, then E is closed.

score 57 · Answer 15 · 2026-04-15 00:59:46

57

Views

Given Lebesgue measurable sets $X,Y,Z$, Show that $f(X,Z)\leq f(X,Y) + f(Y,Z)$

Published on 15 Apr 2026 - 0:59

List Question

prove that $\mathbb{Q}$ can not be $G_{\delta}$ set in $\mathbb{R}$.

If $F \subset \mathbb{R}$ and bounded, then sup $F \in \bar{F}$

Show that Hill's Equation $u'' + a(t)u=0$ if $a(t)<0$ for all $t$ then $u\to\infty$ as $t\to\infty$

Showing that $\Psi: l_1 \rightarrow l_1$ such that $\Psi (u)=v$ where $v_n = \sum^{n}_{p=1}u_pu_{n-p}$ is differentiable.

Is the sum of a Darboux function and a continuous function Darboux?

Generalization of convexity

There is no smooth diffeomorphism $f:\mathbb R^3 \setminus [-\frac{1}{2}, \frac{1}{2}]^3 \to \mathbb R^3$

Sum of series $\sum_1 \frac{\cos(x)^{n-1}}{n!}$

Bound a natural by two consecutive powers

If a normed space is finite dimensional, the unit sphere is compact

Uniform convergence of alternating series

Why does the commutative property of addition not hold for conditionally convergent series?

Describing continuous functions

If ${ X_n }$ is a sequence of real numbers and E = set of all numbers z s.t. $\exists$ a subsequence ${ X_{n_k} }$ convergent to z, then E is closed.

Given Lebesgue measurable sets $X,Y,Z$, Show that $f(X,Z)\leq f(X,Y) + f(Y,Z)$

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