Are $\left\{ (x,y) \in \mathbb{R^2} | |y| > x^2 , |y| < 10 \right\} $ & $\left\{ (x,y) \in \mathbb{R^2}| |y| > x^4 , |y| < 10 \right\} $ homeomorphic?

score 429 · Answer 9 · 2018-11-18 14:53:21

429

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Is a function with an undefined removable discontinuity considered continuous?

Published on 18 Nov 2018 - 14:53

score 652 · Answer 10 · 2018-11-18 15:08:40

652

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How to find what values of $a$ make $f(x)=x^2$ if $x\geq 0$ and $f(x)=ax$ if $x<0$ continuous and differentiable at 0?

Published on 18 Nov 2018 - 15:08

score 113 · Answer 11 · 2026-04-01 10:00:19

113

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Proof that supremum of an almost surely continuous random function is random variable

Published on 01 Apr 2026 - 10:00

score 49 · Answer 12 · 2018-11-18 21:02:31

49

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Determining the points continuity and derivability of a tricky $F: \mathbb{R}^2 \to \mathbb{R}$ function.

Published on 18 Nov 2018 - 21:02

score 162 · Answer 13 · 2018-11-19 01:00:52

162

Views

How to show the function $f\colon z\mapsto\lvert z\rvert^2$ is continuous on the entire complex plane?

Published on 19 Nov 2018 - 1:00

score 264 · Answer 14 · 2018-11-19 05:05:16

264

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If $f$ is monotone increasing on an interval and has a jump discontinuity at $x_0$, show that the jump is bounded above by $f(x_1)-f(x_2)$

Published on 19 Nov 2018 - 5:05

score 133 · Answer 15 · 2026-03-26 23:10:45

133

Views

An element of a set with a finite cover must be an element of at most two open intervals in a subcover?

Published on 26 Mar 2026 - 23:10

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Are $\left\{ (x,y) \in \mathbb{R^2} | |y| > x^2 , |y| < 10 \right\} $ & $\left\{ (x,y) \in \mathbb{R^2}| |y| > x^4 , |y| < 10 \right\} $ homeomorphic?

Is a function with an undefined removable discontinuity considered continuous?

How to find what values of $a$ make $f(x)=x^2$ if $x\geq 0$ and $f(x)=ax$ if $x<0$ continuous and differentiable at 0?

Proof that supremum of an almost surely continuous random function is random variable

Determining the points continuity and derivability of a tricky $F: \mathbb{R}^2 \to \mathbb{R}$ function.

How to show the function $f\colon z\mapsto\lvert z\rvert^2$ is continuous on the entire complex plane?

If $f$ is monotone increasing on an interval and has a jump discontinuity at $x_0$, show that the jump is bounded above by $f(x_1)-f(x_2)$

An element of a set with a finite cover must be an element of at most two open intervals in a subcover?

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