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Everything about Semi-continuity
Property of functions which is weaker than continuity
In mathematical analysis, semicontinuity is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function is upper semicontinuous at a point if, roughly speaking, the function values for arguments near are not much higher than Briefly, a function on a domain is lower semi-continuous if its epigraph is closed in, and upper semi-continuous if is lower semi-continuous. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Semi-continuityA 5-minute orientation
- Skim a recent paper: Semi‐natural habitat, but not aphid amount or continuity, predicts lady beetle abundance across agricultural landscapesInfluential work since 2022
- Pick up a classic book: Continuous semi-Markov processesThe most-reprinted book on the subject
- Read the landmark paper: Semi-Open Sets and Semi-Continuity in Topological SpacesCited 877 times
- Go sideways: Convex analysisA closely related topic
- Go sideways: Continuous functionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Semi-Open Sets and Semi-Continuity in Topological Spaces
Continuity of Generalized Semi-Markov Processes
Points of continuity of semi-continuous functions
Semi-continuity of set-valued monotone mappings
Lower-semi-continuity and area functionals
NOTE ON THE RESULTS WITH LOWER SEMI-CONTINUITY
Semi-open sets, semi-continuity and semi-open mappings in fuzzy bitopological spaces
A unified theory of semi-continuity
🆕 Influential since 2022
Semi‐natural habitat, but not aphid amount or continuity, predicts lady beetle abundance across agricultural landscapes
Attainability and Lower Semi-continuity of the Relative Entropy of Entanglement and Variations on the Theme
Long time dynamics and upper semi-continuity of attractors for piezoelectric beams with nonlinear boundary feedback
Comparison of continuity equation and Gaussian mixture model for long-term density propagation using semi-analytical methods
Upper semi-continuity of numerical attractors for deterministic and random lattice reversible Selkov systems
📚 Books worth reading
Continuous semi-Markov processesBoris Harlamov · 2007- 📕Standard data for arc weldingWelding Institute. · 1975
- 📕Torque converters or transmissionsPeter Martin Heldt · 1942
- 📕No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noiseTorben G. Andersen · 2007
Semi-continuous Braced FramesG.H. Couchman · 1997- 📕Scale-up of the semi-continuous chromatographic processR E. Deeble · 1974
- 📕A Compendium of Semi-continuous Shift Rotas · 1986
- 📕On some applications of semi-continuous functionsW. H. Young · 1909
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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