# 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 T_{2} 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.