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

  1. 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

  1. 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.

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Numerology

  1. Chaldean Numerology

    The numerical value of semicontinuous in Chaldean Numerology is: 6

  2. Pythagorean Numerology

    The numerical value of semicontinuous in Pythagorean Numerology is: 8

Popularity rank by frequency of use

semicontinuous#100000#194244#333333

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"semicontinuous." Definitions.net. STANDS4 LLC, 2024. Web. 19 Mar. 2024. <https://www.definitions.net/definition/semicontinuous>.

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