upper semi-continuous

C2Mathematical Analysis

(technical, academic)Describes a function where, for any point, there exists a neighborhood around that point such that the function values within this neighborhood are not much higher than the function value at the point itself.

Example

• Consider the function f(x) = -1/x for x > 0; it is upper semi-continuous because as x approaches 0, the values of f(x) do not exceed the value at 0.

C2Topological Spaces

(technical, academic)Describes a real-valued function where, for any fixed number, the set of points whose function values are at least that number forms a closed set.