Question

'Adherence' of continuous functions, well-defined and continuous function

score 209 · Answer 1 · 2019-02-25 00:48:12

209

Views

'Adherence' of continuous functions, well-defined and continuous function

Published on 25 Feb 2019 - 0:48

score 301 · Answer 2 · 2019-02-25 19:28:42

301

Views

Topology on the real numbers such that all polynomials are continuous but cosine is not continuous

Published on 25 Feb 2019 - 19:28

score 453 · Answer 3 · 2019-02-26 00:38:38

453

Views

Prove that $C^{\infty}_b(\mathbb{R}^{n})$ is dense in $C_{b}(\mathbb{R}^{n})$ using generic functions.

Published on 26 Feb 2019 - 0:38

score 40 · Answer 4 · 2019-02-26 05:53:39

40

Views

Showing $g:\mathbb{R}^2\rightarrow\mathbb{R}$ is continuously differentiable.

Published on 26 Feb 2019 - 5:53

score 32 · Answer 5 · 2026-03-29 23:48:14

32

Views

Show local uniform convergence for composition of continuous and affine map on compact set.

Published on 29 Mar 2026 - 23:48

score 277 · Answer 6 · 2026-03-26 17:51:48

277

Views

About continuous functions on $p$-adic fields

Published on 26 Mar 2026 - 17:51

score 50 · Answer 7 · 2019-02-26 17:53:24

50

Views

Is $|\sin(x\pi)|$ for $x\in \mathbb{R}$ one of the correct examples of a continuous function which is not differentiable only at integers?

Published on 26 Feb 2019 - 17:53

score 50 · Answer 8 · 2019-02-26 17:56:44

50

Views

Continuity of function with multiple variables

Published on 26 Feb 2019 - 17:56

score 174 · Answer 9 · 2026-04-01 14:36:43

174

Views

Is $ h(x)= \begin{cases} x[\frac{1}{x}] & \text{if } x \neq 0, \\ 1 & \text{if } x=0. \\ \end{cases} $ continuous?

Published on 01 Apr 2026 - 14:36

score 310 · Answer 10 · 2026-04-01 20:48:08

310

Views

Prove that the uniform boundedness principle can be derived from the closed graph theorem.

Published on 01 Apr 2026 - 20:48

score 91 · Answer 11 · 2019-02-26 21:54:49

91

Views

Prove that $f(x)=x^2 \cdot \lfloor {\frac{1}{x^2}}\rfloor$ is continuous.

Published on 26 Feb 2019 - 21:54

score 72 · Answer 12 · 2019-02-27 07:14:07

72

Views

If $f\colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ Then there is a $ c \in [a,b] $ which have this equation for

Published on 27 Feb 2019 - 7:14

score 72 · Answer 13 · 2019-02-27 09:17:24

72

Views

How to prove that $F(g)(x) := \int_{0}^x \cos(\frac{g(t)}{2}) dt$ is continuous?

Published on 27 Feb 2019 - 9:17

score 31 · Answer 14 · 2019-02-27 16:25:04

31

Views

if $f$ is continuous and $t \mapsto \partial_t f(x,t)$ is continuous then is $(x,t) \mapsto \partial_t f(x,t)$ continous?

Published on 27 Feb 2019 - 16:25

score 34 · Answer 15 · 2019-02-27 16:25:20

34

Views

Given a continuous function determine the topology on R.

Published on 27 Feb 2019 - 16:25

List Question

'Adherence' of continuous functions, well-defined and continuous function

Topology on the real numbers such that all polynomials are continuous but cosine is not continuous

Prove that $C^{\infty}_b(\mathbb{R}^{n})$ is dense in $C_{b}(\mathbb{R}^{n})$ using generic functions.

Showing $g:\mathbb{R}^2\rightarrow\mathbb{R}$ is continuously differentiable.

Show local uniform convergence for composition of continuous and affine map on compact set.

About continuous functions on $p$-adic fields

Is $|\sin(x\pi)|$ for $x\in \mathbb{R}$ one of the correct examples of a continuous function which is not differentiable only at integers?

Continuity of function with multiple variables

Is $ h(x)= \begin{cases} x[\frac{1}{x}] & \text{if } x \neq 0, \\ 1 & \text{if } x=0. \\ \end{cases} $ continuous?

Prove that the uniform boundedness principle can be derived from the closed graph theorem.

Prove that $f(x)=x^2 \cdot \lfloor {\frac{1}{x^2}}\rfloor$ is continuous.

If $f\colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ Then there is a $ c \in [a,b] $ which have this equation for

How to prove that $F(g)(x) := \int_{0}^x \cos(\frac{g(t)}{2}) dt$ is continuous?

if $f$ is continuous and $t \mapsto \partial_t f(x,t)$ is continuous then is $(x,t) \mapsto \partial_t f(x,t)$ continous?

Given a continuous function determine the topology on R.

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