List questions from complete-spaces

Published on 16 Apr 2026 - 2:35

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Help understanding the proof that $(C[0,1]), d_\infty$ is complete

Published on 12 Apr 2026 - 14:44

57

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Prove that the limit function is discontinuous

Published on 17 Apr 2026 - 14:38

115

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Any two norms on a finite dimensional $\Bbb K$-linear space are equivalent.

Published on 14 Apr 2026 - 19:06

192

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Compact set and metrizable set.

Published on 13 Apr 2026 - 1:24

1.7k

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Is a nowhere dense set closed?

Published on 10 May 2026 - 14:58

138

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Is $d((a_n),(b_n))=\sum 2^{-n}\lvert a_n-b_n\rvert$ a complete metric on $l^{\infty}$?

Published on 14 Apr 2026 - 23:25

70

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Distance making $(\mathbb{R} \setminus \mathbb{Z},d) $ complete and homeomorphic to $\mathbb{R}\times \mathbb{Z}$

Published on 15 Apr 2026 - 8:54

470

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Explicit absolute value of $\mathbb{C}_p$ and completion of algebraic closure of $\mathbb{F}_p((t))$

Published on 15 Apr 2026 - 1:12

31

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Metric completeness of continuous bounded functions targeting a complete metric space

Published on 11 Apr 2026 - 5:42

54

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Does the completeness of $\mathbb{R}$ mean the metric space $(\mathbb{R},d_E)$ over the field $\mathbb{R}$ complete?

Published on 15 Apr 2026 - 7:07

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Compactness of a metric space

Published on 14 Apr 2026 - 0:42

470

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Why is Baire's theorem called category theorem?

Published on 15 Apr 2026 - 19:18

437

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The completion of $\mathbb{Q}$ with metric $d(x,y) = |x-y|$ (baby Rudin 3.25)

Published on 16 Apr 2026 - 15:58

55

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Proving that $l_∞$ is complete

Published on 10 May 2026 - 15:39

List Question

Find non convergent Cauchy sequence

Help understanding the proof that $(C[0,1]), d_\infty$ is complete

Prove that the limit function is discontinuous

Any two norms on a finite dimensional $\Bbb K$-linear space are equivalent.

Compact set and metrizable set.

Is a nowhere dense set closed?

Is $d((a_n),(b_n))=\sum 2^{-n}\lvert a_n-b_n\rvert$ a complete metric on $l^{\infty}$?

Distance making $(\mathbb{R} \setminus \mathbb{Z},d) $ complete and homeomorphic to $\mathbb{R}\times \mathbb{Z}$

Explicit absolute value of $\mathbb{C}_p$ and completion of algebraic closure of $\mathbb{F}_p((t))$

Metric completeness of continuous bounded functions targeting a complete metric space

Does the completeness of $\mathbb{R}$ mean the metric space $(\mathbb{R},d_E)$ over the field $\mathbb{R}$ complete?

Compactness of a metric space

Why is Baire's theorem called category theorem?

The completion of $\mathbb{Q}$ with metric $d(x,y) = |x-y|$ (baby Rudin 3.25)

Proving that $l_∞$ is complete

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