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1996/1997 On characterizing extendable connectivity functions by associated sets
Harvey Rosen
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Real Anal. Exchange 22(1): 279-283 (1996/1997).


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.


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Harvey Rosen. "On characterizing extendable connectivity functions by associated sets." Real Anal. Exchange 22 (1) 279 - 283, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 1 June 2012

zbMATH: 0879.26012
MathSciNet: MR1433613

Primary: 26A15 , 54C08

Keywords: almost continuous function , associated set , extendable connectivity function , uniform limit

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 1 • 1996/1997
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