List questions from semicontinuous-functions

Published on 18 Jun 2019 - 23:27

109

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If $f$ is LSC, then there exist continuous $g_1\le g_2 \le \dots\to f$ pointwise everywhere.

Published on 30 Jun 2019 - 16:17

297

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Equivalent definitions of semicontinuity

Published on 20 Jul 2019 - 20:37

95

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Which topology is transferred by this specific metric on the rectangle $[0,\infty] \times [0 , \infty ]$?

Published on 27 Jul 2019 - 8:35

277

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Continuous function between a lower semi-continuous function and an upper semi-continuous function.

Published on 29 Jul 2019 - 14:30

177

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Integral of a lsc function is lsc?

Published on 09 Aug 2019 - 16:46

71

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semi-continuous function

Published on 26 Aug 2019 - 11:23

320

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Equality of definitions of Lower Semicontinuity

Published on 11 Sep 2019 - 5:07

2.3k

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Convex closed and unclosed functions and (lower semi)continuity

Published on 28 Apr 2014 - 14:32

2.6k

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Sum of two upper semi continuous functions is upper semi continuous

Published on 03 Aug 2014 - 9:55

616

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Continuity set of a difference of two upper semi-continuous real functions over a metric space

Published on 14 Dec 2014 - 17:29

67

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Show that $\exists \rho\in (a,b)$ such that $f(\rho)\le f(x)$ forall $ x\in (a,b)$.

Published on 02 Oct 2019 - 11:11

212

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upper/lower semi-continuous from topological definition via Example

Published on 15 Oct 2019 - 14:46

38

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Approximate lower semi-continuous functions with uniformly continuous functions

Published on 19 Oct 2019 - 10:41

323

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Why is vitali caratheodory theorem important?

Published on 06 Nov 2019 - 3:42

List Question

Prove that a function is sequentially lower semicontinuous

If $f$ is LSC, then there exist continuous $g_1\le g_2 \le \dots\to f$ pointwise everywhere.

Equivalent definitions of semicontinuity

Which topology is transferred by this specific metric on the rectangle $[0,\infty] \times [0 , \infty ]$?

Continuous function between a lower semi-continuous function and an upper semi-continuous function.

Integral of a lsc function is lsc?

semi-continuous function

Equality of definitions of Lower Semicontinuity

Convex closed and unclosed functions and (lower semi)continuity

Sum of two upper semi continuous functions is upper semi continuous

Continuity set of a difference of two upper semi-continuous real functions over a metric space

Show that $\exists \rho\in (a,b)$ such that $f(\rho)\le f(x)$ forall $ x\in (a,b)$.

upper/lower semi-continuous from topological definition via Example

Approximate lower semi-continuous functions with uniformly continuous functions

Why is vitali caratheodory theorem important?

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