List questions from uniform-convergence

Published on 12 Apr 2026 - 7:42

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Suppose $f_{k}$ defined on $\mathbb{R}^n$ converge uniformly to a function $f$. Each $f_{n}$ is bounded, say by $A_{k}$. Prove that $f$ is bounded.

Published on 16 Apr 2026 - 11:51

184

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Suppose $f_{n}$ in $C[0,1]$ all have Lipschitz constant $L$. Show that if $f_{n}$ converges pointwise to $f$, then the convergence is uniform

Published on 16 Apr 2026 - 2:32

198

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How to visualize Dini theorem regarding sequence of functions?

Published on 13 Apr 2026 - 20:49

42

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Uniformly Bounded Functions of Hyperreals

Published on 10 May 2026 - 13:49

251

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Uniform convergence of a continuously parametrized family of functions

Published on 11 Apr 2026 - 20:13

41

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Convergence depending on step

Published on 14 Apr 2026 - 22:53

90

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If $f_n,f$ are holomorphic and $f_n\to f$ uniformly on compacta, then $f'_n\to f'$ uniformly on compacta

Published on 17 Apr 2026 - 5:04

43

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Let $f_{n}(x) = \frac{\arctan(nx)}{\sqrt{n}}$ show that it converges uniformly to $f$ - Proof Verification

Published on 15 Apr 2026 - 12:40

38

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Convergence in $L^∞(\mathbb{R})$

Published on 13 Apr 2026 - 11:11

200

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Prove that the sequence $\{f_n\}_{n \in \mathbb{N}}$ is uniformly convergent on a compact space $X$

Published on 17 Apr 2026 - 3:47

2.6k

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Pointwise convergence of uniformly continuous functions to zero, but not uniformly

Published on 11 Apr 2026 - 17:17

67

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Uniform convergence on interval.

Published on 14 Apr 2026 - 3:55

42

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Uniform convergent in $C_0$

Published on 11 Apr 2026 - 17:12

253

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I have a question on Complex Analysis, probably on Normal families or Schwartz Lemma

Published on 14 Apr 2026 - 6:18

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Differentiation of a product of Sobolev functions

Suppose $f_{k}$ defined on $\mathbb{R}^n$ converge uniformly to a function $f$. Each $f_{n}$ is bounded, say by $A_{k}$. Prove that $f$ is bounded.

Suppose $f_{n}$ in $C[0,1]$ all have Lipschitz constant $L$. Show that if $f_{n}$ converges pointwise to $f$, then the convergence is uniform

How to visualize Dini theorem regarding sequence of functions?

Uniformly Bounded Functions of Hyperreals

Uniform convergence of a continuously parametrized family of functions

Convergence depending on step

If $f_n,f$ are holomorphic and $f_n\to f$ uniformly on compacta, then $f'_n\to f'$ uniformly on compacta

Let $f_{n}(x) = \frac{\arctan(nx)}{\sqrt{n}}$ show that it converges uniformly to $f$ - Proof Verification

Convergence in $L^∞(\mathbb{R})$

Prove that the sequence $\{f_n\}_{n \in \mathbb{N}}$ is uniformly convergent on a compact space $X$

Pointwise convergence of uniformly continuous functions to zero, but not uniformly

Uniform convergence on interval.

Uniform convergent in $C_0$

I have a question on Complex Analysis, probably on Normal families or Schwartz Lemma

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