Question

Are those two subsets of $\mathcal{C}^0([0,1],\mathbb{R})$ equal?

score 96 · Answer 1 · 2018-01-21 17:12:05

96

Views

Are those two subsets of $\mathcal{C}^0([0,1],\mathbb{R})$ equal?

Published on 21 Jan 2018 - 17:12

score 102 · Answer 2 · 2026-03-27 07:26:58

102

Views

An exercise on continuous functions

Published on 27 Mar 2026 - 7:26

score 94 · Answer 3 · 2018-01-22 06:54:32

94

Views

If $f$ is differentiable and monotonic on $ [a,b] $, is $f'$ continuous on $ [a,b] $?

Published on 22 Jan 2018 - 6:54

score 28 · Answer 4 · 2026-03-25 03:02:47

28

Views

$ g\in C^{2}(\Omega)$ are dense in $f\in C(\partial\Omega)$?

Published on 25 Mar 2026 - 3:02

score 73 · Answer 5 · 2018-01-22 13:45:05

73

Views

determine possible values of a which k is a continuous function and differentiable function

Published on 22 Jan 2018 - 13:45

score 193 · Answer 6 · 2026-03-25 18:51:48

193

Views

Is a projection f(x,y)=x producing an open set out of an open set, every closed set to a closed set and every compact set to a compact set?

Published on 25 Mar 2026 - 18:51

score 49 · Answer 7 · 2026-03-25 06:13:26

49

Views

$f$ Riemann int; $\exists$ cont. fcn. $g$ s.t $\int |f(x)-g(x)| dx < \epsilon$. Show supp $g$ can be taken to be arbitrarily small nbhd of supp $f$.

Published on 25 Mar 2026 - 6:13

score 42 · Answer 8 · 2018-01-23 05:18:37

42

Views

Show $z\mapsto\frac{\exp(\exp(z+z^2+z^3))}{1+z\overline{z}}$ is continuous on $\mathbb{C}$ and takes on the value $3$.

Published on 23 Jan 2018 - 5:18

score 804 · Answer 9 · 2018-01-23 15:49:09

804

Views

Fundamental theorem of calculus with finitely many discontinuities

Published on 23 Jan 2018 - 15:49

score 96 · Answer 10 · 2026-03-24 19:52:34

96

Views

Existence of the Differential of a multi-variable function

Published on 24 Mar 2026 - 19:52

score 1.2k · Answer 11 · 2026-03-24 23:42:05

1.2k

Views

Composite functions, continuity, and limits

Published on 24 Mar 2026 - 23:42

score 175 · Answer 12 · 2018-01-24 04:31:25

175

Views

What properties of functions are preserved under pointwise limits?

Published on 24 Jan 2018 - 4:31

score 1.2k · Answer 13 · 2018-01-24 05:13:49

1.2k

Views

How can the following be false based on the information about continuous functions?

Published on 24 Jan 2018 - 5:13

score 400 · Answer 14 · 2026-03-24 22:01:58

400

Views

Prove that if $f$ lies in $L^{1}({\bf R}^{n})$ then $\widehat f$ is uniformly continuous on ${\bf R}^{n},$

Published on 24 Mar 2026 - 22:01

score 326 · Answer 15 · 2026-03-27 03:44:08

326

Views

Is D = $\{ (x,y,z) \in \mathbb{R}^3 \vert x^2 + y^2 +z^2 = 1, 0 < z < 1 \}$ homeomorphic to $S^1$ and to $\mathbb{R}^2\setminus \{(0,0)\}$

Published on 27 Mar 2026 - 3:44

List Question

Are those two subsets of $\mathcal{C}^0([0,1],\mathbb{R})$ equal?

An exercise on continuous functions

If $f$ is differentiable and monotonic on $ [a,b] $, is $f'$ continuous on $ [a,b] $?

$ g\in C^{2}(\Omega)$ are dense in $f\in C(\partial\Omega)$?

determine possible values of a which k is a continuous function and differentiable function

Is a projection f(x,y)=x producing an open set out of an open set, every closed set to a closed set and every compact set to a compact set?

$f$ Riemann int; $\exists$ cont. fcn. $g$ s.t $\int |f(x)-g(x)| dx < \epsilon$. Show supp $g$ can be taken to be arbitrarily small nbhd of supp $f$.

Show $z\mapsto\frac{\exp(\exp(z+z^2+z^3))}{1+z\overline{z}}$ is continuous on $\mathbb{C}$ and takes on the value $3$.

Fundamental theorem of calculus with finitely many discontinuities

Existence of the Differential of a multi-variable function

Composite functions, continuity, and limits

What properties of functions are preserved under pointwise limits?

How can the following be false based on the information about continuous functions?

Prove that if $f$ lies in $L^{1}({\bf R}^{n})$ then $\widehat f$ is uniformly continuous on ${\bf R}^{n},$

Is D = $\{ (x,y,z) \in \mathbb{R}^3 \vert x^2 + y^2 +z^2 = 1, 0 < z < 1 \}$ homeomorphic to $S^1$ and to $\mathbb{R}^2\setminus \{(0,0)\}$

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