## Real Analysis Exchange

### On characterizing extendable connectivity functions by associated sets

Harvey Rosen

#### Abstract

We answer two questions asked by Rosen in 1994. We show that the class of extendable connectivity functions from $I$ into $I$ ($I = [0,1]$) cannot be characterized in terms of associated sets, and we show that one of Jones’ functions obeying $f(x+y) = f(x) + f(y)$ is an example of an almost continuous function from $\mathbb{R}$ into $\mathbb{R}$ which is not the uniform limit of any sequence of extendable connectivity functions.

#### Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 279-283.

Dates
First available in Project Euclid: 1 June 2012

https://projecteuclid.org/euclid.rae/1338515220

Mathematical Reviews number (MathSciNet)
MR1433613

Zentralblatt MATH identifier
0879.26012

#### Citation

Rosen, Harvey. On characterizing extendable connectivity functions by associated sets. Real Anal. Exchange 22 (1996), no. 1, 279--283. https://projecteuclid.org/euclid.rae/1338515220

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