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Semi- Continuity
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Geliefert zwischen Do., 05.02.2026 und Fr., 06.02.2026
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High Quality Content by WIKIPEDIA articles! In mathematical analysis, semi-continuity (or semicontinuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f is upper (lower) semi-continuous at a point x0 if, roughly speaking, the function values for arguments near x0 are either close to f(x0) or less than (greater than) f(x0).Consider the function f, piecewise defined by f(x) = 1 for x 0 and f(x) = 1 for x 0. This function is upper semi-continuous at x0 = 0, but not lower semi-continuous.A function is continuous at x0 if and only if it is upper and lower semi-continuous there. Therefore, semi-continuity can be used to prove continuity. If f and g are two real-valued functions which are both upper semi-continuous at x0, then so is f + g. If both functions are non-negative, then the product function fg will also be upper semi-continuous at x0. Multiplying a positive upper semi-continuous function with a negative number turns it into a lower semi-continuous function.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131120749
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131120749
- Format Fachbuch
- Titel Semi- Continuity
- Herausgeber Betascript Publishing
- Anzahl Seiten 96
- Genre Mathematik
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