Question

Is $C([0,T] ; L^1(\mathbb{R}^{N}) \cap L^{\infty}(\mathbb{R}^{N}))$ a Complete Metric Space? (For Using Banach Fixed Point Theorem)

score 81 · Answer 1 · 2026-03-27 00:03:43

81

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Is $C([0,T] ; L^1(\mathbb{R}^{N}) \cap L^{\infty}(\mathbb{R}^{N}))$ a Complete Metric Space? (For Using Banach Fixed Point Theorem)

Published on 27 Mar 2026 - 0:03

score 337 · Answer 2 · 2026-04-01 15:40:02

337

Views

Heine borel theorem doesn't hold

Published on 01 Apr 2026 - 15:40

score 78 · Answer 3 · 2019-09-27 15:10:28

78

Views

Closure in a metric space

Published on 27 Sep 2019 - 15:10

score 63 · Answer 4 · 2026-03-26 04:51:08

63

Views

$(E,d)$ a metric space, $S\subseteq E$ closed implies $(S,d)$ complete - is this true?

Published on 26 Mar 2026 - 4:51

score 36 · Answer 5 · 2019-09-28 00:38:10

36

Views

What does it mean if my computed values for a metric is negative?

Published on 28 Sep 2019 - 0:38

score 285 · Answer 6 · 2026-04-09 02:27:47

285

Views

Understanding Partition of Unity

Published on 09 Apr 2026 - 2:27

score 1.3k · Answer 7 · 2026-04-10 22:30:47

1.3k

Views

Definition of Lipschitz continuous function in the general case

Published on 10 Apr 2026 - 22:30

score 128 · Answer 8 · 2026-03-26 08:00:33

128

Views

Prove that the space of left translation of $C(G)$ is a $T_0$ space

Published on 26 Mar 2026 - 8:00

score 69 · Answer 9 · 2026-03-25 15:59:54

69

Views

Circumradius of trigonic

Published on 25 Mar 2026 - 15:59

score 727 · Answer 10 · 2026-04-11 17:01:57

727

Views

Proof that a subspace of a complete metric space is complete iff closed

Published on 11 Apr 2026 - 17:01

score 1.6k · Answer 11 · 2019-09-29 09:35:55

1.6k

Views

What is a practical use for this metric?

Published on 29 Sep 2019 - 9:35

score 522 · Answer 12 · 2026-04-09 02:27:11

522

Views

Understanding clopen sets

Published on 09 Apr 2026 - 2:27

score 134 · Answer 13 · 2019-09-29 20:13:04

134

Views

Let $\mathit f:X_1 \to X_2$ be continuous and surjective. With certain property of $d$, if $(X_1, d_1)$ is complete, then is $(X_2,d_2)$ complete?

Published on 29 Sep 2019 - 20:13

score 35 · Answer 14 · 2026-03-29 03:44:29

35

Views

Showing boundedness in $\mathbb{R}^2$ implies totally boundedness

Published on 29 Mar 2026 - 3:44

score 197 · Answer 15 · 2026-03-27 01:44:32

197

Views

Prove $\mathit f(x)=x$ for some $x\in\mathbb R$.

Published on 27 Mar 2026 - 1:44

List Question

Is $C([0,T] ; L^1(\mathbb{R}^{N}) \cap L^{\infty}(\mathbb{R}^{N}))$ a Complete Metric Space? (For Using Banach Fixed Point Theorem)

Heine borel theorem doesn't hold

Closure in a metric space

$(E,d)$ a metric space, $S\subseteq E$ closed implies $(S,d)$ complete - is this true?

What does it mean if my computed values for a metric is negative?

Understanding Partition of Unity

Definition of Lipschitz continuous function in the general case

Prove that the space of left translation of $C(G)$ is a $T_0$ space

Circumradius of trigonic

Proof that a subspace of a complete metric space is complete iff closed

What is a practical use for this metric?

Understanding clopen sets

Let $\mathit f:X_1 \to X_2$ be continuous and surjective. With certain property of $d$, if $(X_1, d_1)$ is complete, then is $(X_2,d_2)$ complete?

Showing boundedness in $\mathbb{R}^2$ implies totally boundedness

Prove $\mathit f(x)=x$ for some $x\in\mathbb R$.

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