List questions from continuity

Published on 08 Apr 2026 - 16:35

97

Views

Continuity of $f(x)=\frac{|x|\sqrt{x^4+y^2}}{|x|+|y|},$ when $(x,y)\neq 0$ and $0$ otherwise

Published on 10 Feb 2019 - 15:04

33

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What does it mean for a map taking a measure to an integral to be continuous?

Published on 29 Mar 2026 - 1:35

548

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How to show if $f(c) > 0$ there exist a neighborhood over which $f(x)>0$?

Published on 12 Feb 2019 - 3:40

46

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Continuity in a point in a metric space

Published on 06 Apr 2026 - 13:32

108

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Counterexample for Hausdorff Assumption is removed

Published on 28 Mar 2026 - 10:03

2.9k

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Shouldn't tan(x) be a continuous function

Published on 13 Feb 2019 - 10:06

29

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Is this mapping from a hypercube into a Banach space of continuous functions itself continuous?

Published on 28 Mar 2026 - 11:15

46

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An example of some functions.(continuous, differentiable)

Published on 13 Feb 2019 - 21:14

134

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equivalence of arg max for continuous functions

Published on 14 Feb 2019 - 0:19

149

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Confusion in definition of limit and continuity

Published on 14 Feb 2019 - 14:52

544

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Is $\sum\limits_{n=1}^\infty \arctan \frac x {n^2}$ continuous?

Published on 25 Mar 2026 - 23:37

332

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Can you prove mean value theorem using IVT?

Published on 15 Feb 2019 - 4:05

89

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Preimage of $\partial\Omega$ under a continuous function

Published on 15 Feb 2019 - 20:38

79

Views

$\varepsilon$-$\delta$-proof that $3|x| − 2$ is continuous at $x = 0$

Published on 26 Mar 2026 - 17:52

List Question

Study the continuity of a function

Continuity of $f(x)=\frac{|x|\sqrt{x^4+y^2}}{|x|+|y|},$ when $(x,y)\neq 0$ and $0$ otherwise

What does it mean for a map taking a measure to an integral to be continuous?

How to show if $f(c) > 0$ there exist a neighborhood over which $f(x)>0$?

Continuity in a point in a metric space

Counterexample for Hausdorff Assumption is removed

Shouldn't tan(x) be a continuous function

Is this mapping from a hypercube into a Banach space of continuous functions itself continuous?

An example of some functions.(continuous, differentiable)

equivalence of arg max for continuous functions

Confusion in definition of limit and continuity

Is $\sum\limits_{n=1}^\infty \arctan \frac x {n^2}$ continuous?

Can you prove mean value theorem using IVT?

Preimage of $\partial\Omega$ under a continuous function

$\varepsilon$-$\delta$-proof that $3|x| − 2$ is continuous at $x = 0$

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