Functions Essentially Depending on at Most One Variable

✍ Scribed by Ilijas Farah

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 119 KB
• Volume: 94
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.2000.3129

✦ Synopsis

In this note we analyze the question: When does a function f : | d Ä | essentially depend on at most one coordinate? (Here |=N _ [0].) For example, the function

depends on both variables. However, we can cover its domain by two rectangles, 2|_| and (2|+1)_|, such that f depends on at most one variable on each one of them. Definition 1. A function f : X d Ä X is elementary if its domain can be covered by finitely many rectangles such that f depends on at most one coordinate on each one of them. (By rectangle we mean a set of the form

A function from a subset of X d is elementary if it can be extended to an elementary function.