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Semi-continuity

In mathematical analysis, semicontinuity (or semi-continuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f {\displaystyle f} is upper (respectively, lower) semicontinuous at a point x 0 {\displaystyle x_{0}} if, roughly speaking, the function values for arguments near x 0…

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Semicontinuity of set-valued functions

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Semi-continuity

Nodes137
Edges136
Triples8
Avg. degree1.99
Density0.014599
Components1

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displaystyle semicontinuous function lower upper functions mathbb space set semicontinuity point closed convex topological defined continuous infty analysis set-valued overline

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SubjectPredicateObjectConfidenceSrc
Tonelli's theorem in functional analysisinstance ofThis is often combined with results0.80text
which characterizes the weak lower semicontinuity of nonlinear functionals on Lp spaces in terms of the convexity of another functioninstance ofThis is often combined with results0.80text
dimensioninstance ofis upper semicontinuous.Vakil collected a list of further semicontinuity results in algebraic geometry.Descriptive set theorySemicontinuous functions are used in descriptive set…0.80text
rankinstance ofis upper semicontinuous.Vakil collected a list of further semicontinuity results in algebraic geometry.Descriptive set theorySemicontinuous functions are used in descriptive set…0.80text
or ordinal heightinstance ofis upper semicontinuous.Vakil collected a list of further semicontinuity results in algebraic geometry.Descriptive set theorySemicontinuous functions are used in descriptive set…0.80text
dimensioninstance ofDescriptive set theorySemicontinuous functions are used in descriptive set theory to define stratifications of topological spaces by complexity measures0.80text
rankinstance ofDescriptive set theorySemicontinuous functions are used in descriptive set theory to define stratifications of topological spaces by complexity measures0.80text
or ordinal heightinstance ofDescriptive set theorySemicontinuous functions are used in descriptive set theory to define stratifications of topological spaces by complexity measures0.80text

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