List questions from uniform-convergence

Published on 30 Mar 2026 - 11:37

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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 23 Feb 2026 - 17:27

181

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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 23 Feb 2026 - 17:27

195

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How to visualize Dini theorem regarding sequence of functions?

Published on 21 Jul 2019 - 10:59

41

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Uniformly Bounded Functions of Hyperreals

Published on 24 Mar 2026 - 23:44

248

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Uniform convergence of a continuously parametrized family of functions

Published on 24 Jul 2019 - 9:24

38

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Convergence depending on step

Published on 26 Jul 2019 - 16:40

87

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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 27 Jul 2019 - 17:59

41

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

Published on 28 Jul 2019 - 0:10

35

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Convergence in $L^∞(\mathbb{R})$

Published on 28 Jul 2019 - 2:58

197

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

Published on 28 Jul 2019 - 7:25

2.6k

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

Published on 24 Mar 2026 - 19:49

65

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Uniform convergence on interval.

Published on 28 Jul 2019 - 14:51

41

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Uniform convergent in $C_0$

Published on 24 Mar 2026 - 20:45

250

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

Published on 28 Jul 2019 - 19:00

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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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