semikontinuous

Semikontinuous is a term used in mathematics, particularly in the context of functions and sequences. It refers to a function or sequence that is continuous at all but a finite number of points. In other words, a semikontinuous function or sequence has a finite number of discontinuities, after which it is continuous.

This concept is particularly useful in analysis and topology. For example, in the study of real-valued functions, a semikontinuous function is one that is continuous except at a finite number of points. This property allows for the application of various theorems and techniques that rely on continuity, while still accommodating the presence of discontinuities.

In the context of sequences, a semikontinuous sequence is one that is continuous except at a finite number of terms. This can be relevant in areas such as numerical analysis and discrete mathematics, where sequences are often studied in relation to their continuity properties.

The term "semikontinuous" is not as widely recognized as terms like "continuous" or "discontinuous," but it is a useful concept in specialized areas of mathematics. It provides a way to describe functions and sequences that are mostly continuous, with a few exceptions, which can be important for understanding their behavior and properties.