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What (who) is upper semicontinuous function - definition

PROPERTY OF FUNCTIONS WEAKER THAN CONTINUITY

Semicontinuous; Semicontinuity; Semi-continuous; Lower semi-continuous; Upper semi-continuous; Lower semicontinuous; Upper semicontinuous; Semi-continuous function; Semi-continuous mapping; Semicontinuous function; Upper-semicontinuous; Upper semicontinuity; Lower semicontinuity; Upper semi-continuity; Lower semi-continuity

$A lower semicontinuous function that is not upper semicontinuous. The solid blue dot indicates <math>f\left(x_0\right).</math>$
$An upper semicontinuous function that is not lower semicontinuous. The solid blue dot indicates <math>f\left(x_0\right).</math>$

Function (mathematics)

$A binary operation is a typical example of a bivariate function which assigns to each pair <math>(x, y)</math> the result <math>x\circ y</math>.$

ASSOCIATION OF A SINGLE OUTPUT TO EACH INPUT

Mathematical Function; Mathematical function; Function specification (mathematics); Mathematical functions; Empty function; Function (math); Ambiguous function; Function (set theory); Function (Mathematics); Functions (mathematics); Domain and range; Functional relationship; G(x); H(x); Function notation; Output (mathematics); Ƒ(x); Overriding (mathematics); Overriding union; F of x; Function of x; Bivariate function; Functional notation; Function of several variables; Y=f(x); ⁡; Draft:The Repeating Fractional Function; Image (set theory); Mutivariate function; Draft:Specifying a function; Function (maths); Functions (math); Functions (maths); F(x); Empty map; Function evaluation

In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously.

https://en.wikipedia.org/wiki/Function_(mathematics)

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 is upper (respectively, lower) semicontinuous at a point x_0 if, roughly speaking, the function values for arguments near x_0 are not much higher (respectively, lower) than f\left(x_0\right).

https://en.wikipedia.org/wiki/Semi-continuity

Upper school

IN ENGLAND, SCHOOLS WITHIN SECONDARY EDUCATION; SECTION OF A LARGER SCHOOL

Upper School; Upper schools

Upper schools in the UK are usually schools within secondary education. Outside England, the term normally refers to a section of a larger school.

https://en.wikipedia.org/wiki/Upper_school

Wikipedia

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 $f$ is upper (respectively, lower) semicontinuous at a point $x_{0}$ if, roughly speaking, the function values for arguments near $x_{0}$ are not much higher (respectively, lower) than $f\left(x_{0}\right).$

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 $x_{0}$ to $f\left(x_{0}\right)+c$ for some $c>0$ , then the result is upper semicontinuous; if we decrease its value to $f\left(x_{0}\right)-c$ 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.

https://en.wikipedia.org/wiki/Semi-continuity