Question

Find a function defined on $[0,1]$, valued on an interval, but is discontinuous at each point.

score 96 · Answer 1 · 2018-09-20 22:55:52

96

Views

Find a function defined on $[0,1]$, valued on an interval, but is discontinuous at each point.

Published on 20 Sep 2018 - 22:55

score 119 · Answer 2 · 2026-03-30 00:19:22

119

Views

connected set of sum of upper semi continuous function

Published on 30 Mar 2026 - 0:19

score 21 · Answer 3 · 2018-09-21 11:44:04

21

Views

Continuity of functional in $E\subset C^1([0,1])$

Published on 21 Sep 2018 - 11:44

score 53 · Answer 4 · 2018-09-21 14:30:43

53

Views

Does the formula $f(x,y)=(x^2-y)yx^{-4}\mathbf 1_{0<y<x^2}$ define a continuous function?

Published on 21 Sep 2018 - 14:30

score 49 · Answer 5 · 2018-09-21 15:07:57

49

Views

Why would $f(x)$ at point $b$ not equal $f(b)$?

Published on 21 Sep 2018 - 15:07

score 78 · Answer 6 · 2018-09-21 16:01:16

78

Views

Prove continuity of two variable function

Published on 21 Sep 2018 - 16:01

score 108 · Answer 7 · 2018-09-21 18:18:09

108

Views

Is $g(x)= \frac{x}{1-\left | x \right |}$ uniformly continuous?

Published on 21 Sep 2018 - 18:18

score 807 · Answer 8 · 2026-04-04 10:08:20

807

Views

Show that the function $h$ defined by $h(x)=g(f(x))$ is lower semicontinuous.

Published on 04 Apr 2026 - 10:08

score 60 · Answer 9 · 2026-03-25 20:40:06

60

Views

Using uniform continuity

Published on 25 Mar 2026 - 20:40

score 253 · Answer 10 · 2026-04-01 14:05:08

253

Views

Continuity property for a closed set

Published on 01 Apr 2026 - 14:05

score 435 · Answer 11 · 2026-03-26 14:43:08

435

Views

Proving that $f(x)= \sin (2\pi x [ x])$ is not uniformly continuous on $\mathbb{R}$

Published on 26 Mar 2026 - 14:43

score 62 · Answer 12 · 2018-09-23 06:37:50

62

Views

Let $f$ be continuous on $[a,b]$, be differentiable on $(a,b)$.

Published on 23 Sep 2018 - 6:37

score 114 · Answer 13 · 2018-09-23 11:25:13

114

Views

Extend $f(x )= \frac{|x^2-4|}{x^2-4}$ in a way that $f(x)$ is continuous

Published on 23 Sep 2018 - 11:25

score 97 · Answer 14 · 2018-09-23 13:43:48

97

Views

Extend $f(x)=\frac{6x^3-11x^2-16x-4}{2x^2-5x-2}$ in a way it is continuous $\forall x \in \mathbb{R}$

Published on 23 Sep 2018 - 13:43

score 165 · Answer 15 · 2026-03-25 20:42:12

165

Views

Prove $\frac{\sqrt{x}}{x-1}$ is continuous on (0,1)

Published on 25 Mar 2026 - 20:42

List Question

Find a function defined on $[0,1]$, valued on an interval, but is discontinuous at each point.

connected set of sum of upper semi continuous function

Continuity of functional in $E\subset C^1([0,1])$

Does the formula $f(x,y)=(x^2-y)yx^{-4}\mathbf 1_{0<y<x^2}$ define a continuous function?

Why would $f(x)$ at point $b$ not equal $f(b)$?

Prove continuity of two variable function

Is $g(x)= \frac{x}{1-\left | x \right |}$ uniformly continuous?

Show that the function $h$ defined by $h(x)=g(f(x))$ is lower semicontinuous.

Using uniform continuity

Continuity property for a closed set

Proving that $f(x)= \sin (2\pi x [ x])$ is not uniformly continuous on $\mathbb{R}$

Let $f$ be continuous on $[a,b]$, be differentiable on $(a,b)$.

Extend $f(x )= \frac{|x^2-4|}{x^2-4}$ in a way that $f(x)$ is continuous

Extend $f(x)=\frac{6x^3-11x^2-16x-4}{2x^2-5x-2}$ in a way it is continuous $\forall x \in \mathbb{R}$

Prove $\frac{\sqrt{x}}{x-1}$ is continuous on (0,1)

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