Question

(X,d) be a metric space. $F: X\to \overline{\mathbb{R}}$. $F$ is sequentially lower semicontinuous iff $F$ is lower semicontinuous

score 51 · Answer 1 · 2023-05-09 08:29:16

51

Views

(X,d) be a metric space. $F: X\to \overline{\mathbb{R}}$. $F$ is sequentially lower semicontinuous iff $F$ is lower semicontinuous

Published on 09 May 2023 - 8:29

score 106 · Answer 2 · 2023-05-09 12:44:41

106

Views

$F$ is lower semicontinuous $\iff F(x)=\sup_{r>0}\inf_{y\in B(x,r)}F(y)$ for all $x\in X$

Published on 09 May 2023 - 12:44

score 17 · Answer 3 · 2023-05-14 14:37:26

17

Views

Show that $\mathbb{I}_A$ is a lower semi continuous function for an open set $A$ in $\mathbb{R}$

Published on 14 May 2023 - 14:37

score 115 · Answer 4 · 2023-05-16 08:33:40

115

Views

Lim inf with norm and weak convergence[follow up]

Published on 16 May 2023 - 8:33

score 60 · Answer 5 · 2023-05-21 21:34:05

60

Views

Image of lower semi-continuous function on lower-bounded sets

Published on 21 May 2023 - 21:34

score 42 · Answer 6 · 2023-05-23 19:03:55

42

Views

A question about a normal lower semicontinuos function

Published on 23 May 2023 - 19:03

score 24 · Answer 7 · 2023-06-15 23:20:24

24

Views

In a regular top space, is it true that for every $x \in X$ and closed set $C \subseteq X$, $\exists$ open nbh of x $G$ s.t $\overline{G}\subset C^C$?

Published on 15 Jun 2023 - 23:20

score 31 · Answer 8 · 2026-02-23 04:20:36

31

Views

How do we know that the maximum/minimum is attainable in the definition of viscosity solution?

Published on 23 Feb 2026 - 4:20

score 41 · Answer 9 · 2023-09-12 16:30:13

41

Views

If $f(x):=\mu(\overline{B}(x,r))$ show that $f$ is upper semicontinuous

Published on 12 Sep 2023 - 16:30

score 129 · Answer 10 · 2023-10-23 13:50:04

129

Views

Lower Semicontinuity of $L^p$ norms with varying exponents

Published on 23 Oct 2023 - 13:50

score 32 · Answer 11 · 2023-12-03 18:27:54

32

Views

Uniform Convergence of Lagrange function defined for $q-$absolutely continuous curves

Published on 03 Dec 2023 - 18:27

score 87 · Answer 12 · 2023-12-13 19:07:47

87

Views

Why is the $\Sigma$-product of unit intervals pseudocompact?

Published on 13 Dec 2023 - 19:07

score 49 · Answer 13 · 2024-02-02 12:34:51

49

Views

Weakly lower-semicontinuous functional on $L^2$

Published on 02 Feb 2024 - 12:34

score 63 · Answer 14 · 2024-02-08 00:45:53

63

Views

upper semicontinuous definitions

Published on 08 Feb 2024 - 0:45

score 37 · Answer 15 · 2024-02-23 19:51:26

37

Views

Confused about lower semicontinuous functions

Published on 23 Feb 2024 - 19:51

List Question

(X,d) be a metric space. $F: X\to \overline{\mathbb{R}}$. $F$ is sequentially lower semicontinuous iff $F$ is lower semicontinuous

$F$ is lower semicontinuous $\iff F(x)=\sup_{r>0}\inf_{y\in B(x,r)}F(y)$ for all $x\in X$

Show that $\mathbb{I}_A$ is a lower semi continuous function for an open set $A$ in $\mathbb{R}$

Lim inf with norm and weak convergence[follow up]

Image of lower semi-continuous function on lower-bounded sets

A question about a normal lower semicontinuos function

In a regular top space, is it true that for every $x \in X$ and closed set $C \subseteq X$, $\exists$ open nbh of x $G$ s.t $\overline{G}\subset C^C$?

How do we know that the maximum/minimum is attainable in the definition of viscosity solution?

If $f(x):=\mu(\overline{B}(x,r))$ show that $f$ is upper semicontinuous

Lower Semicontinuity of $L^p$ norms with varying exponents

Uniform Convergence of Lagrange function defined for $q-$absolutely continuous curves

Why is the $\Sigma$-product of unit intervals pseudocompact?

Weakly lower-semicontinuous functional on $L^2$

upper semicontinuous definitions

Confused about lower semicontinuous functions

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