List questions from complete-spaces

Published on 06 Aug 2018 - 15:49

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

Published on 09 Aug 2018 - 14:32

52

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Prove that the limit function is discontinuous

Published on 13 Aug 2018 - 2:33

112

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

Published on 18 Aug 2018 - 17:13

188

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Compact set and metrizable set.

Published on 25 Aug 2018 - 17:25

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Is a nowhere dense set closed?

Published on 01 Sep 2018 - 6:52

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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 04 Sep 2018 - 12:43

67

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

Published on 04 Sep 2018 - 15:12

467

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

Published on 05 Sep 2018 - 15:08

28

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Metric completeness of continuous bounded functions targeting a complete metric space

Published on 16 Sep 2018 - 19:41

51

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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 17 Sep 2018 - 15:36

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Compactness of a metric space

Published on 21 Sep 2018 - 7:53

467

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Why is Baire's theorem called category theorem?

Published on 24 Sep 2018 - 12:30

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

Published on 26 Sep 2018 - 5:41

51

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Proving that $l_∞$ is complete

Published on 29 Sep 2018 - 6:59

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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