List questions from continuity

Published on 06 Apr 2026 - 1:19

39

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Commutativity of Diagram in Top "Lift-like property but for covers"

Published on 25 Mar 2026 - 4:41

82

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Why should there is a $c\in [0,1]$: $f(c)=f(c+1)$.

Published on 04 Jun 2019 - 6:01

116

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Conclude $\left\|f_n-f\right\|_\infty\to0$ from knowing that $f_n(x_n)\to f(x)$ for all $(x_n)$ and $x$

Published on 01 Apr 2026 - 1:38

321

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Are of Polynomials of Continuous functions complete?

Published on 09 Apr 2026 - 6:17

58

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How to show this function involving min is continuous?

Published on 10 Apr 2026 - 4:11

102

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Show that $(Tf_{n})_{n}$ is equicontinuous

Published on 09 Apr 2026 - 15:22

1.1k

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Proof that $f$ is continuous if and only if $f$ composed with projections is continuous

Published on 13 Apr 2026 - 2:18

146

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Does the following imply Lipschitz continuity?

Published on 12 Apr 2026 - 2:40

99

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Is $f(x,y)=\sin{(x)}+\sin{(y)}$ continuous on $\mathbb{R}^2$?

Published on 11 Apr 2026 - 12:51

279

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For $E$ a finite-dimensional Banach Space, there exists an orthonormal basis.

Published on 26 Mar 2026 - 4:31

46

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Is there a sequence $(f_n)_n \subset C_b(\mathbb{R})$ with $f_n \to f \in C_b(\mathbb{R})$ pointwise but $f_n(1/n) \not \to f(0)$?

Published on 11 Apr 2026 - 10:38

33

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Continuity criteria for a function between two vector spaces

Published on 06 Jun 2019 - 21:58

355

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I want to know what was the motivation/intuition behind weierstrass function?

Published on 29 Mar 2026 - 20:15

109

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How do I apply Intermediate Value theorem correctly?

Published on 09 Apr 2026 - 4:58

List Question

Piecewise Continuity and Integrability...

Commutativity of Diagram in Top "Lift-like property but for covers"

Why should there is a $c\in [0,1]$: $f(c)=f(c+1)$.

Conclude $\left\|f_n-f\right\|_\infty\to0$ from knowing that $f_n(x_n)\to f(x)$ for all $(x_n)$ and $x$

Are of Polynomials of Continuous functions complete?

How to show this function involving min is continuous?

Show that $(Tf_{n})_{n}$ is equicontinuous

Proof that $f$ is continuous if and only if $f$ composed with projections is continuous

Does the following imply Lipschitz continuity?

Is $f(x,y)=\sin{(x)}+\sin{(y)}$ continuous on $\mathbb{R}^2$?

For $E$ a finite-dimensional Banach Space, there exists an orthonormal basis.

Is there a sequence $(f_n)_n \subset C_b(\mathbb{R})$ with $f_n \to f \in C_b(\mathbb{R})$ pointwise but $f_n(1/n) \not \to f(0)$?

Continuity criteria for a function between two vector spaces

I want to know what was the motivation/intuition behind weierstrass function?

How do I apply Intermediate Value theorem correctly?

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