Question

Continuous function on $[0,1]$ such that its zeros form a nowhere dense set of positive measure?

score 431 · Answer 1 · 2026-04-10 13:49:07

431

Views

Continuous function on $[0,1]$ such that its zeros form a nowhere dense set of positive measure?

Published on 10 Apr 2026 - 13:49

score 34 · Answer 2 · 2019-04-19 05:25:10

34

Views

Prove that $y_1=y_2$ or $\{x \in [a,b] \mid y_1(x)=y_2(x)\}$ is finite

Published on 19 Apr 2019 - 5:25

score 33 · Answer 3 · 2026-04-11 06:17:57

33

Views

Doubt about definition of continuity involving open ball.

Published on 11 Apr 2026 - 6:17

score 318 · Answer 4 · 2026-03-26 04:51:17

318

Views

Continuity and Lipschitz Property of Infimal Convolution

Published on 26 Mar 2026 - 4:51

score 158 · Answer 5 · 2026-03-30 06:29:07

158

Views

Uniform Convergence and continuity (Rudin 7.4)

Published on 30 Mar 2026 - 6:29

score 27 · Answer 6 · 2019-04-21 04:39:48

27

Views

Showing that $f: D_1(0) \subset \mathbb{R}^2 \to \mathbb{R}, f(x) = \frac{1}{1- \|x\| }$ is continuous

Published on 21 Apr 2019 - 4:39

score 83 · Answer 7 · 2019-04-21 06:03:08

83

Views

For continuously differentiable $f,$ is it true that the set $\{(x_0,x_1)\in (0,1)^2: |f(x_0)| + |f'(x_1)| \geq \epsilon\}$ not compact in $(0,1)^2?$

Published on 21 Apr 2019 - 6:03

score 292 · Answer 8 · 2019-04-21 10:03:11

292

Views

Is continuity necessary to establish $f(x+r) =f(x) +f(r), r\in\Bbb Q \Rightarrow f(x+y) =f(x) +f(y) $

Published on 21 Apr 2019 - 10:03

score 142 · Answer 9 · 2026-04-11 11:46:40

142

Views

Divergence in supremum norm implies divergence on whole segment

Published on 11 Apr 2026 - 11:46

score 33 · Answer 10 · 2026-04-03 21:30:48

33

Views

Is the function $f(x) = \sum_{n\geq 1 } \cos(n^2 x ) / n^{2.6}$ absolutely continuous?

Published on 03 Apr 2026 - 21:30

score 59 · Answer 11 · 2026-03-26 08:02:38

59

Views

For an increasing function $f$, if $f(y_n)-f(x_n) \to 0$ , then $f$ is continuous at $0$

Published on 26 Mar 2026 - 8:02

score 104 · Answer 12 · 2026-04-03 04:03:14

104

Views

Do not understand: "A real function $f$ is continuous if $f^{-1}(O)$ is open for each open set $O$"

Published on 03 Apr 2026 - 4:03

score 245 · Answer 13 · 2019-04-22 11:46:24

245

Views

Prove that $f: \mathbb{R} \rightarrow \mathbb{R}$ is continuous iff $f^{-1}(O)$ is open for each open set $O$

Published on 22 Apr 2019 - 11:46

score 116 · Answer 14 · 2026-04-07 17:51:39

116

Views

If $f:[0,1]\to \mathbb{C} $ be continuous with $f(0)=0$ and $f(1)=2$, then $|f(t_0)|=1$ for some $t_0 \in [0,1]$

Published on 07 Apr 2026 - 17:51

score 144 · Answer 15 · 2026-03-27 10:46:15

144

Views

Step in the proof of the continuity of the Gauss Gamma function

Published on 27 Mar 2026 - 10:46

List Question

Continuous function on $[0,1]$ such that its zeros form a nowhere dense set of positive measure?

Prove that $y_1=y_2$ or $\{x \in [a,b] \mid y_1(x)=y_2(x)\}$ is finite

Doubt about definition of continuity involving open ball.

Continuity and Lipschitz Property of Infimal Convolution

Uniform Convergence and continuity (Rudin 7.4)

Showing that $f: D_1(0) \subset \mathbb{R}^2 \to \mathbb{R}, f(x) = \frac{1}{1- \|x\| }$ is continuous

For continuously differentiable $f,$ is it true that the set $\{(x_0,x_1)\in (0,1)^2: |f(x_0)| + |f'(x_1)| \geq \epsilon\}$ not compact in $(0,1)^2?$

Is continuity necessary to establish $f(x+r) =f(x) +f(r), r\in\Bbb Q \Rightarrow f(x+y) =f(x) +f(y) $

Divergence in supremum norm implies divergence on whole segment

Is the function $f(x) = \sum_{n\geq 1 } \cos(n^2 x ) / n^{2.6}$ absolutely continuous?

For an increasing function $f$, if $f(y_n)-f(x_n) \to 0$ , then $f$ is continuous at $0$

Do not understand: "A real function $f$ is continuous if $f^{-1}(O)$ is open for each open set $O$"

Prove that $f: \mathbb{R} \rightarrow \mathbb{R}$ is continuous iff $f^{-1}(O)$ is open for each open set $O$

If $f:[0,1]\to \mathbb{C} $ be continuous with $f(0)=0$ and $f(1)=2$, then $|f(t_0)|=1$ for some $t_0 \in [0,1]$

Step in the proof of the continuity of the Gauss Gamma function

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