List questions from continuity

Published on 16 Mar 2026 - 17:15

39

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Continuity of quotient map at $\infty/\infty$

Published on 17 Mar 2026 - 10:42

61

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Properties of functions on topological spaces

Published on 26 Mar 2026 - 12:40

234

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Continuity of the function $f(x)=\lim\limits_{n \to \infty}[\lim\limits_{t\to 0}[\frac{\sin^2 (n!\pi x)}{\sin^2(n! \pi x)+t^2}]] $, $x \in \mathbb R$

Published on 12 Mar 2026 - 12:49

214

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Can connectedness preservation be used to define continuity of a function?

Published on 20 Mar 2026 - 23:14

1k

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Show that $(x^2 + y^2) \sin\left(\frac{1}{x^2 + y^2}\right)$ is differentiable.

Published on 21 Mar 2026 - 10:07

182

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If a continuous function is bigger than another at a point, then it is so in an entire neighbourhood...proof?

Published on 25 Mar 2026 - 1:17

45

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multivariable continuous

Published on 21 Mar 2026 - 20:29

376

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Continuous function with parameter

Published on 16 Mar 2026 - 22:24

62

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Is ${C}[0,1],\Bbb{R}$ homeomorphic to any $\Bbb{R^n}$, for an integer $n$?

Published on 28 Mar 2026 - 18:43

265

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f from sorgenfrey line to R which is continuous

Published on 26 Mar 2026 - 21:05

603

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I want to know every single bit there is to understand in this following proof

Published on 26 Mar 2026 - 2:19

891

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Check my proof that continuous linear functionals are bounded

Published on 26 Mar 2026 - 6:00

58

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Proving $f(x)$ is onto using maxima/minima

Published on 25 Mar 2026 - 1:22

747

Views

Equivalence for a reversed Lipschitz-type condition

Published on 28 Mar 2026 - 4:44

List Question

Restriction of function

Continuity of quotient map at $\infty/\infty$

Properties of functions on topological spaces

Continuity of the function $f(x)=\lim\limits_{n \to \infty}[\lim\limits_{t\to 0}[\frac{\sin^2 (n!\pi x)}{\sin^2(n! \pi x)+t^2}]] $, $x \in \mathbb R$

Can connectedness preservation be used to define continuity of a function?

Show that $(x^2 + y^2) \sin\left(\frac{1}{x^2 + y^2}\right)$ is differentiable.

If a continuous function is bigger than another at a point, then it is so in an entire neighbourhood...proof?

multivariable continuous

Continuous function with parameter

Is ${C}[0,1],\Bbb{R}$ homeomorphic to any $\Bbb{R^n}$, for an integer $n$?

f from sorgenfrey line to R which is continuous

I want to know every single bit there is to understand in this following proof

Check my proof that continuous linear functionals are bounded

Proving $f(x)$ is onto using maxima/minima

Equivalence for a reversed Lipschitz-type condition

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