Question

IF $\Psi(x) = \inf_{0 \leq s \leq t} \Phi_s(x)$,can we have $\Psi^{-1}(x) = \sup_{0 \leq s \leq t} \Phi_s^{-1}(x)$?

score 18 · Answer 1 · 2026-03-19 20:39:13

18

Views

IF $\Psi(x) = \inf_{0 \leq s \leq t} \Phi_s(x)$,can we have $\Psi^{-1}(x) = \sup_{0 \leq s \leq t} \Phi_s^{-1}(x)$?

Published on 19 Mar 2026 - 20:39

score 33 · Answer 2 · 2023-12-19 14:37:02

33

Views

Bounded holomorphic function attaching supremum and infimum through vertical lines

Published on 19 Dec 2023 - 14:37

score 118 · Answer 3 · 2023-12-21 12:10:04

118

Views

Are there alternatives to Rudin's proof that $\sup \{ p\in\mathbb{ Q}^+\mid p^2<2 \} =\sqrt 2$?

Published on 21 Dec 2023 - 12:10

score 204 · Answer 4 · 2026-03-29 18:32:26

204

Views

Why we assume the least upper bound property to be true?

Published on 29 Mar 2026 - 18:32

score 37 · Answer 5 · 2023-12-26 09:28:41

37

Views

Real Analysis - Proof writing style(Supremum Proof)

Published on 26 Dec 2023 - 9:28

score 203 · Answer 6 · 2023-12-27 06:44:53

203

Views

Application on Lindeberg's condition

Published on 27 Dec 2023 - 6:44

score 95 · Answer 7 · 2026-03-25 09:43:48

95

Views

How to show that geodesic curvature of isoperimetric set is constant

Published on 25 Mar 2026 - 9:43

score 37 · Answer 8 · 2023-12-28 17:19:13

37

Views

EDITED: If $u_n$ is bounded in $L^2$ and $|F(x, u_n)|\le c_1 +c_2 |u_n|^{p-1}$, does $\sup_{n\in\mathbb N}\int_{K}|F(x, u_n)|^2 dx<\infty$ hold?

Published on 28 Dec 2023 - 17:19

score 118 · Answer 9 · 2023-12-30 12:31:37

118

Views

Showing that a given function satisfies certain properties. Related to Lebesgue integral, limits and supremums.

Published on 30 Dec 2023 - 12:31

score 41 · Answer 10 · 2024-01-06 05:22:19

Does the set of integral of all possible step functions under a curve have maximum element? Or it only has supremum with no maximum element?

score 56 · Answer 11 · 2024-01-06 12:27:56

56

Views

What is the reasoning behind this rigorous proof of the infimum of $A$?

Published on 06 Jan 2024 - 12:27

score 48 · Answer 12 · 2026-03-25 12:15:15

48

Views

Show that $f_n$ is an increasing $e$-uniform Cauchy sequence

Published on 25 Mar 2026 - 12:15

score 46 · Answer 13 · 2024-01-12 01:56:54

46

Views

Logical notation for suprema and infima

Published on 12 Jan 2024 - 1:56

score 66 · Answer 14 · 2024-01-13 10:05:15

66

Views

$\{r\in \mathbb Q \mid r^2 <2 \}$ has $\{r\in \mathbb Q \mid r^2 >2 \}$ as its set of upper bounds

Published on 13 Jan 2024 - 10:05

score 354 · Answer 15 · 2024-01-14 12:39:31

354

Views

Finding supremum of a given function, over a given domain.

Published on 14 Jan 2024 - 12:39

List Question

IF $\Psi(x) = \inf_{0 \leq s \leq t} \Phi_s(x)$,can we have $\Psi^{-1}(x) = \sup_{0 \leq s \leq t} \Phi_s^{-1}(x)$?

Bounded holomorphic function attaching supremum and infimum through vertical lines

Are there alternatives to Rudin's proof that $\sup \{ p\in\mathbb{ Q}^+\mid p^2<2 \} =\sqrt 2$?

Why we assume the least upper bound property to be true?

Real Analysis - Proof writing style(Supremum Proof)

Application on Lindeberg's condition

How to show that geodesic curvature of isoperimetric set is constant

EDITED: If $u_n$ is bounded in $L^2$ and $|F(x, u_n)|\le c_1 +c_2 |u_n|^{p-1}$, does $\sup_{n\in\mathbb N}\int_{K}|F(x, u_n)|^2 dx<\infty$ hold?

Showing that a given function satisfies certain properties. Related to Lebesgue integral, limits and supremums.

Does the set of integral of all possible step functions under a curve have maximum element? Or it only has supremum with no maximum element?

What is the reasoning behind this rigorous proof of the infimum of $A$?

Show that $f_n$ is an increasing $e$-uniform Cauchy sequence

Logical notation for suprema and infima

$\{r\in \mathbb Q \mid r^2 <2 \}$ has $\{r\in \mathbb Q \mid r^2 >2 \}$ as its set of upper bounds

Finding supremum of a given function, over a given domain.

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