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Upper semicontinuous functions to $\mathbb{N}$ are locally constant on a dense subset

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#general-topology #semicontinuous-functions
280
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Show that support function of any set in $\mathbb{R}^n$ is lower semi-continuous function.

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#functional-analysis #functions #convergence-divergence #metric-spaces #semicontinuous-functions
447
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Functional is weak lower semicontinuous but not weak continuous

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#real-analysis #functional-analysis #calculus-of-variations #functional-inequalities #semicontinuous-functions
1.3k
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Lower semi continuous envelope is lower semi continuous

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#real-analysis #calculus-of-variations #semicontinuous-functions
158
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Upper semicontinuous function as a poinwise limit of continuous fuctions

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#general-topology #pointwise-convergence #semicontinuous-functions
433
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Proximal Gradient Method Justification - Why Does It Work?

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#optimization #convex-analysis #gradient-descent #proximal-operators #semicontinuous-functions
85
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Do separately semi-continuous functions have a dense set of semi-continuities?

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#general-topology #reference-request #product-space #continuity #semicontinuous-functions
2.8k
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Show that lower semi-continuous function attains it's minimum. (Proof verification) (By contradiction)

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#real-analysis #proof-verification #upper-lower-bounds #semicontinuous-functions
76
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Silly question on lower semi-continuity

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#metric-spaces #convex-analysis #convex-optimization #limsup-and-liminf #semicontinuous-functions
77
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How far from a matrix the rank does not decrease?

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#matrix-calculus #matrix-decomposition #matrix-rank #svd #semicontinuous-functions
32
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An inequality about compact functions and lsc functions

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#real-analysis #measure-theory #proof-explanation #semicontinuous-functions
581
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Why the length is lower semi-continuous?

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#metric-spaces #metric-geometry #semicontinuous-functions
198
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Reference for extreme value theorem.

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#general-topology #analysis #reference-request #semicontinuous-functions #extreme-value-theorem
182
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Is the inf-convolution of two continuous functions continuous?

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#real-analysis #measure-theory #continuity #semicontinuous-functions
555
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Conjugate Function Is Lower Semicontinuous

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#functional-analysis #analysis #functions #vector-spaces #semicontinuous-functions

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