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Article 9

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:

 

  • Question 7

How may the functions of the form f º g, where f is an absolutely continuous homeomorphism and g is differentiable, be characterized?

  • Question 6

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?

  • Question 1

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.