What does semicontinuous mean?
Definitions for semicontinuous
semi·con·tin·u·ous
This dictionary definitions page includes all the possible meanings, example usage and translations of the word semicontinuous.
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Wiktionary
semicontinuousadjective
(of a function) That it is continuous almost everywhere, except at certain points at which it is either upper semi-continuous or lower semi-continuous.
Wikipedia
semicontinuous
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 {\displaystyle x_{0}} are not much higher (respectively, lower) than f ( x 0 ) . {\displaystyle f\left(x_{0}\right).} A function is continuous if and only if it is both upper and lower semicontinuous. If we take a continuous function and increase its value at a certain point x 0 {\displaystyle x_{0}} to f ( x 0 ) + c {\displaystyle f\left(x_{0}\right)+c} for some c > 0 {\displaystyle c>0} , then the result is upper semicontinuous; if we decrease its value to f ( x 0 ) − c {\displaystyle f\left(x_{0}\right)-c} then the result is lower semicontinuous. The notion of upper and lower semicontinuous function was first introduced and studied by René Baire in his thesis in 1899.
Numerology
Chaldean Numerology
The numerical value of semicontinuous in Chaldean Numerology is: 6
Pythagorean Numerology
The numerical value of semicontinuous in Pythagorean Numerology is: 8
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"semicontinuous." Definitions.net. STANDS4 LLC, 2024. Web. 23 Dec. 2024. <https://www.definitions.net/definition/semicontinuous>.
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