Question

Proof for continuity of $h(x) = \begin{cases} x, & x\in\mathbb{Q} \\ -x, & x\notin\mathbb{Q} \end{cases}$

score 111 · Answer 1 · 2018-12-08 18:59:48

111

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Proof for continuity of $h(x) = \begin{cases} x, & x\in\mathbb{Q} \\ -x, & x\notin\mathbb{Q} \end{cases}$

Published on 08 Dec 2018 - 18:59

score 67 · Answer 2 · 2018-12-08 20:05:21

67

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Is $f(x,y) = \frac{x^ny^m}{x^{n'}+y^{m'}}$ continuous at origin?

Published on 08 Dec 2018 - 20:05

score 133 · Answer 3 · 2026-03-26 01:03:35

133

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Show that $ \lim_{n\to\infty} \int_{0}^{1} f_n $ exists

Published on 26 Mar 2026 - 1:03

score 1.1k · Answer 4 · 2018-12-09 06:16:03

1.1k

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Is every real valued continuous function on $(0,1)$ is uniformly continuous?

Published on 09 Dec 2018 - 6:16

score 127 · Answer 5 · 2018-12-09 14:10:21

127

Views

$f(\mathbb{Q}) \subset \mathbb{R} - \mathbb{Q}$ and $f(\mathbb{R} - \mathbb{Q}) \subset \mathbb{Q}$

Published on 09 Dec 2018 - 14:10

score 1.9k · Answer 6 · 2026-03-26 21:35:35

1.9k

Views

Uniform Continuity in Topological Spaces?

Published on 26 Mar 2026 - 21:35

score 66 · Answer 7 · 2026-02-23 04:56:22

66

Views

Analyse Equicontinuity (uniform continuity) of a function $ \frac{\sin(x)}{x},\; x > 0 $

Published on 23 Feb 2026 - 4:56

score 1.2k · Answer 8 · 2026-03-28 06:45:02

1.2k

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Riemann integrability if the set of discontinuities has finitely many accumulation points

Published on 28 Mar 2026 - 6:45

score 296 · Answer 9 · 2026-03-25 01:17:09

296

Views

Discretization of continuous model with white noise to use Kalman filter later

Published on 25 Mar 2026 - 1:17

score 137 · Answer 10 · 2018-12-10 01:00:22

137

Views

When is a sum of continuous functions continuous?

Published on 10 Dec 2018 - 1:00

score 72 · Answer 11 · 2018-12-10 02:56:14

How can I show $f_{n}(x) = \sqrt{x^{2} + \frac{1}{n}}$ is continuously differentiable on $x \in ]-1,+1[$ for each $n \in \mathbb{N}$?

score 63 · Answer 12 · 2018-12-10 06:35:57

63

Views

Twice diffrentiable function $f: \mathbb R \to \mathbb R$ such that $f''(x)+e^xf(x)=0, \forall x \in \mathbb R$

Published on 10 Dec 2018 - 6:35

score 452 · Answer 13 · 2026-03-30 21:54:46

452

Views

Does existence of mixed derivative imply continuity?

Published on 30 Mar 2026 - 21:54

score 117 · Answer 14 · 2026-03-26 14:24:58

117

Views

Space filling curves: Hilbert vs Peano

Published on 26 Mar 2026 - 14:24

score 45 · Answer 15 · 2026-03-25 17:51:42

45

Views

Lipschitz functions are $o(|x|)$?

Published on 25 Mar 2026 - 17:51

List Question

Proof for continuity of $h(x) = \begin{cases} x, & x\in\mathbb{Q} \\ -x, & x\notin\mathbb{Q} \end{cases}$

Is $f(x,y) = \frac{x^ny^m}{x^{n'}+y^{m'}}$ continuous at origin?

Show that $ \lim_{n\to\infty} \int_{0}^{1} f_n $ exists

Is every real valued continuous function on $(0,1)$ is uniformly continuous?

$f(\mathbb{Q}) \subset \mathbb{R} - \mathbb{Q}$ and $f(\mathbb{R} - \mathbb{Q}) \subset \mathbb{Q}$

Uniform Continuity in Topological Spaces?

Analyse Equicontinuity (uniform continuity) of a function $ \frac{\sin(x)}{x},\; x > 0 $

Riemann integrability if the set of discontinuities has finitely many accumulation points

Discretization of continuous model with white noise to use Kalman filter later

When is a sum of continuous functions continuous?

How can I show $f_{n}(x) = \sqrt{x^{2} + \frac{1}{n}}$ is continuously differentiable on $x \in ]-1,+1[$ for each $n \in \mathbb{N}$?

Twice diffrentiable function $f: \mathbb R \to \mathbb R$ such that $f''(x)+e^xf(x)=0, \forall x \in \mathbb R$

Does existence of mixed derivative imply continuity?

Space filling curves: Hilbert vs Peano

Lipschitz functions are $o(|x|)$?

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