List questions from complete-spaces

Published on 30 Oct 2018 - 20:28

188

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Complete space?

Published on 03 Nov 2018 - 18:23

189

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Boundary and completion of the metric space $c_{00}$

Published on 05 Nov 2018 - 2:53

48

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Completeness of variation on $L_2$-space

Published on 09 Nov 2018 - 7:02

1.3k

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Continuous function $f:X\to X$ such that $d(f(x), f(y)) < d(x, y)$ whenever $x\neq y$, has a fixed point in complete metric space.

Published on 25 Mar 2026 - 10:25

42

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$\{u_m\}$ is bounded in $W^{1, p}(U)$, but does not possess a (norm-)convergent sequence in $L^{p^∗}(U)$

Published on 15 Nov 2018 - 1:01

135

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Show that (X,d) is complete

Published on 18 Nov 2018 - 20:40

318

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Any Cauchy net in metric space is convergent?

Published on 25 Mar 2026 - 6:21

831

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Equivalence of Baire Category Theorem for Complete Metric Spaces.

Published on 21 Nov 2018 - 12:32

216

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Tightness of a finite measure on a complete and separable metric space

Published on 25 Nov 2018 - 4:46

230

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Is the following set a compact set?

Published on 25 Mar 2026 - 9:48

381

Views

Locally Complete Metric Space

Published on 26 Nov 2018 - 22:06

392

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Prove a closed subset of a complete metric space is complete via contradiction

Published on 28 Nov 2018 - 5:57

55

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Proof $d(A \cup B,C) = \max\{d(A,C),d(B,C)\}$ in any complete metric space

Published on 30 Nov 2018 - 19:12

82

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Is this set meager? $A = \{x\in \mathbb{R}: \exists c>0, |x-j2^{-k}|\geq c2^{-k}, \forall j\in \mathbb{Z}, k\geq 0 \}$

Published on 01 Dec 2018 - 5:03

List Question

Using the sequence definitions, if $X$ is compact, prove that $X$ is complete

Complete space?

Boundary and completion of the metric space $c_{00}$

Completeness of variation on $L_2$-space

Continuous function $f:X\to X$ such that $d(f(x), f(y)) < d(x, y)$ whenever $x\neq y$, has a fixed point in complete metric space.

$\{u_m\}$ is bounded in $W^{1, p}(U)$, but does not possess a (norm-)convergent sequence in $L^{p^∗}(U)$

Show that (X,d) is complete

Any Cauchy net in metric space is convergent?

Equivalence of Baire Category Theorem for Complete Metric Spaces.

Tightness of a finite measure on a complete and separable metric space

Is the following set a compact set?

Locally Complete Metric Space

Prove a closed subset of a complete metric space is complete via contradiction

Proof $d(A \cup B,C) = \max\{d(A,C),d(B,C)\}$ in any complete metric space

Is this set meager? $A = \{x\in \mathbb{R}: \exists c>0, |x-j2^{-k}|\geq c2^{-k}, \forall j\in \mathbb{Z}, k\geq 0 \}$

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