## Real Analysis Exchange

### On the Almost Continuity of the Diagonal of Functions

#### Abstract

In this paper we consider the following questions: Under what additional assumptions is the diagonal $f\triangle g$ of almost continuous functions vanishing on the set of discontinuity points of an almost continuous function, too. Moreover, one can show that the facts considered (diagonals and ac-homotopies) can be applied to the characterization of continuity or the investigations of the algebraic operations on almost continuous functions.

#### Article information

Source
Real Anal. Exchange, Volume 23, Number 2 (1999), 459-470.

Dates
First available in Project Euclid: 14 May 2012

https://projecteuclid.org/euclid.rae/1337001358

Mathematical Reviews number (MathSciNet)
MR1639948

Zentralblatt MATH identifier
0943.26008

Subjects
Primary: 26A15; 54C08

#### Citation

Doliwa, Dariusz; Pawlak, Ryszard Jerzy. On the Almost Continuity of the Diagonal of Functions. Real Anal. Exchange 23 (1999), no. 2, 459--470. https://projecteuclid.org/euclid.rae/1337001358