Question

Why must $f$ have a negative value?

score 75 · Answer 1 · 2026-04-07 17:51:13

Why must $f$ have a negative value?

Published on 07 Apr 2026 - 17:51

score 52 · Answer 2 · 2019-02-04 01:35:30

Suppose $f : [0,1] \rightarrow \mathbb{R}^2$ is continuous and injective, then show that $f([0,1])$ has an empty interior in $(\mathbb{R}^2, d_e)$.

score 32 · Answer 3 · 2026-03-25 22:26:40

32

Views

How to demonstrate the uniform continuity of a function in the case it has no limited derivative

Published on 25 Mar 2026 - 22:26

score 89 · Answer 4 · 2026-03-27 10:12:07

89

Views

Continuity at $(0,0)$ of $f(x,y)=\frac{x^3+y^3}{x-y}, \; \;(x,y)\neq(0,0)$, otherwise $0$

Published on 27 Mar 2026 - 10:12

score 274 · Answer 5 · 2019-02-04 17:57:16

274

Views

Continuity of the integral depending on parameter

Published on 04 Feb 2019 - 17:57

score 1.7k · Answer 6 · 2019-02-04 19:14:43

1.7k

Views

Example of bijective continuous function that is not homeomorphism

Published on 04 Feb 2019 - 19:14

score 716 · Answer 7 · 2019-02-04 20:18:23

716

Views

The set of discontinuities of an increasing right continuous function is closed.

Published on 04 Feb 2019 - 20:18

score 51 · Answer 8 · 2019-02-05 03:53:14

51

Views

Is $I(t)=\int_{0}^{\pi/2} (x-\pi/2)\exp\bigl(-t\sec(x)\bigr) dx$ continuous?

Published on 05 Feb 2019 - 3:53

score 33 · Answer 9 · 2026-04-06 10:18:49

33

Views

$V\colon \mathcal{B}(X, \mathbb{R}) \rightarrow \mathcal{B}(X, \mathbb{R})$, $V(f) = |f|$ is continuous

Published on 06 Apr 2026 - 10:18

score 321 · Answer 10 · 2019-02-06 05:26:37

321

Views

Continuous function defined on (0,1) to {0,1}

Published on 06 Feb 2019 - 5:26

score 735 · Answer 11 · 2026-03-26 01:03:20

735

Views

On the smooth dependence on initial conditions for the following ODE

Published on 26 Mar 2026 - 1:03

score 65 · Answer 12 · 2026-03-27 06:17:05

65

Views

Is the function $ f \colon X \to f(X), f(x) =x^3 $ continuous, uniformly continuous

Published on 27 Mar 2026 - 6:17

score 112 · Answer 13 · 2026-04-07 20:17:06

112

Views

Is f continuous at $ x = \pm 2 $ and everywhere else it isn't continuous?

Published on 07 Apr 2026 - 20:17

score 122 · Answer 14 · 2026-04-06 10:15:11

122

Views

Discrete metric space and continuity.

Published on 06 Apr 2026 - 10:15

score 137 · Answer 15 · 2019-02-06 18:02:18

137

Views

Prove there exists a delta

Published on 06 Feb 2019 - 18:02

List Question

Why must $f$ have a negative value?

Suppose $f : [0,1] \rightarrow \mathbb{R}^2$ is continuous and injective, then show that $f([0,1])$ has an empty interior in $(\mathbb{R}^2, d_e)$.

How to demonstrate the uniform continuity of a function in the case it has no limited derivative

Continuity at $(0,0)$ of $f(x,y)=\frac{x^3+y^3}{x-y}, \; \;(x,y)\neq(0,0)$, otherwise $0$

Continuity of the integral depending on parameter

Example of bijective continuous function that is not homeomorphism

The set of discontinuities of an increasing right continuous function is closed.

Is $I(t)=\int_{0}^{\pi/2} (x-\pi/2)\exp\bigl(-t\sec(x)\bigr) dx$ continuous?

$V\colon \mathcal{B}(X, \mathbb{R}) \rightarrow \mathcal{B}(X, \mathbb{R})$, $V(f) = |f|$ is continuous

Continuous function defined on (0,1) to {0,1}

On the smooth dependence on initial conditions for the following ODE

Is the function $ f \colon X \to f(X), f(x) =x^3 $ continuous, uniformly continuous

Is f continuous at $ x = \pm 2 $ and everywhere else it isn't continuous?

Discrete metric space and continuity.

Prove there exists a delta

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