## Real Analysis Exchange

### Sums of Quasicontinuous Functions with Closed Graphs

#### Abstract

We prove that every real-valued $\mathcal{B}^*_1$ function $f$ defined on a~separable metric space $X$ is the sum of three quasicontinuous functions with closed graphs, and there is a $\mathcal{B}^*_1$ function which is not the sum of two quasicontinuous functions with closed graphs. Consequently, if $X$ is a separable metric space which is a Baire space in the strong sense, then the next three properties are equivalent: (1)$f$ is a $\mathcal{B}^*_1$ function, (2) $f$ is the sum of (at least) three quasicontinuous functions with closed graphs, and (3) $f$ is a piecewise continuous function.

#### Article information

Source
Real Anal. Exchange Volume 25, Number 2 (1999), 679-690.

Dates
First available in Project Euclid: 3 January 2009

https://projecteuclid.org/euclid.rae/1230995403

Mathematical Reviews number (MathSciNet)
MR1778521

Zentralblatt MATH identifier
1021.54015

Subjects
Primary: 54C08: Weak and generalized continuity