Answers to three questions of Foran
Real Analysis Exchange 14 (1989), 43-24
Mathematical reviews subject classification: 26A30, 26A46
Abstract
In the article Continuous functions (Real Analysis Exchange 2 (1977), 85-103), James Foran asked 12 questions.
Here we give answers to the following three:
How may the functions of the form f º g, where f is an absolutely continuous homeomorphism and g is differentiable, be characterized?
How can the class of functions of the form f º g, where f is a homeomorphism and g satisfies Banach's condition T2 and is continuous, be characterized?
Can every ACG* and continuous function be written as f º g, where f is differentiable and g is monotone and absolutely continuous?
Theorem 1, Theorem 2 and Theorem 3 are answers to these three questions.
