Question

The metric space $(L^0 (X), \rho)$ of $\mu$-measurable functions is complete

score 52 · Answer 1 · 2023-08-16 10:51:11

52

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The metric space $(L^0 (X), \rho)$ of $\mu$-measurable functions is complete

Published on 16 Aug 2023 - 10:51

score 40 · Answer 2 · 2023-08-18 01:16:32

40

Views

The metric $\hat \rho (f, g) := \inf_{\delta >0} \{ \mu (|f - g| > \delta) +\delta \}$ on the space of $\mu$-measurable functions is complete

Published on 18 Aug 2023 - 1:16

score 63 · Answer 3 · 2026-03-27 12:27:41

63

Views

Range of a function on subintervals

Published on 27 Mar 2026 - 12:27

score 35 · Answer 4 · 2026-03-26 14:41:58

35

Views

Boundedness of Linear Operators on Banach Subspace with Different Norm

Published on 26 Mar 2026 - 14:41

score 125 · Answer 5 · 2026-02-23 06:34:52

125

Views

Completion of operator space

Published on 23 Feb 2026 - 6:34

score 27 · Answer 6 · 2026-03-25 18:56:29

27

Views

On Elkik's Theorem of Henselian pair.

Published on 25 Mar 2026 - 18:56

score 38 · Answer 7 · 2023-09-05 16:43:24

38

Views

Prove that the limit of the sequences corresponding to the image of two sequences converging to the same point is the same.

Published on 05 Sep 2023 - 16:43

score 74 · Answer 8 · 2023-09-06 14:40:12

74

Views

Question in Construction for Proof of Nested Sphere Theorem

Published on 06 Sep 2023 - 14:40

score 139 · Answer 9 · 2026-02-25 04:19:41

139

Views

Why is $C([0;1])$ with the supremum metric complete, but it is not with the integral metric

Published on 25 Feb 2026 - 4:19

score 42 · Answer 10 · 2026-02-27 18:17:06

42

Views

$(M,d)$ complete metric space and $f : M \longrightarrow M$ such that $f^p$ is a contraction. Then, $lim f^n(x) = a$, for any $x \in M$.

Published on 27 Feb 2026 - 18:17

score 84 · Answer 11 · 2023-10-05 14:12:19

84

Views

Show that $C([0, 1])$ equipped with $\Vert f\Vert_1:=\int_0^1|f(x)|dx$ is not complete

Published on 05 Oct 2023 - 14:12

score 71 · Answer 12 · 2023-10-10 03:31:23

71

Views

The completion of metric spaces with bounded sequences instead of Cauchy sequences

Published on 10 Oct 2023 - 3:31

score 70 · Answer 13 · 2023-10-10 16:41:01

70

Views

In a complete space $X$ is every $x \in X$ the limit of a sequence $\{x_n\}$ such that $x \not\in \{x_n\}$?

Published on 10 Oct 2023 - 16:41

score 116 · Answer 14 · 2023-10-15 14:42:42

116

Views

A distance function on a Riemannian manifold which can be viewed as a distance function to the point at infinity.

Published on 15 Oct 2023 - 14:42

score 39 · Answer 15 · 2023-10-31 12:24:38

39

Views

Is space complete and separable?

Published on 31 Oct 2023 - 12:24

List Question

The metric space $(L^0 (X), \rho)$ of $\mu$-measurable functions is complete

The metric $\hat \rho (f, g) := \inf_{\delta >0} \{ \mu (|f - g| > \delta) +\delta \}$ on the space of $\mu$-measurable functions is complete

Range of a function on subintervals

Boundedness of Linear Operators on Banach Subspace with Different Norm

Completion of operator space

On Elkik's Theorem of Henselian pair.

Prove that the limit of the sequences corresponding to the image of two sequences converging to the same point is the same.

Question in Construction for Proof of Nested Sphere Theorem

Why is $C([0;1])$ with the supremum metric complete, but it is not with the integral metric

$(M,d)$ complete metric space and $f : M \longrightarrow M$ such that $f^p$ is a contraction. Then, $lim f^n(x) = a$, for any $x \in M$.

Show that $C([0, 1])$ equipped with $\Vert f\Vert_1:=\int_0^1|f(x)|dx$ is not complete

The completion of metric spaces with bounded sequences instead of Cauchy sequences

In a complete space $X$ is every $x \in X$ the limit of a sequence $\{x_n\}$ such that $x \not\in \{x_n\}$?

A distance function on a Riemannian manifold which can be viewed as a distance function to the point at infinity.

Is space complete and separable?

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