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2005/2006 Closed relations and equivalence classes of quasicontinuous functions.
Annalisa Crannell, Marc Frantz, Michelle LeMasurier
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Real Anal. Exchange 31(2): 409-423 (2005/2006).


This paper introduces a notion of equivalence that links closed relations and quasicontinuous functions; we examine classes of quasicontinuous functions that have the same set of continuity points. In doing so, we show that every minimal closed relation is the closure of a quasicontinuous function and vice-versa. We also show that this notion is of use in dynamical systems. Every quasicontinuous function is equivalent to one that is measurable, and under certain circumstances---in fact, under just those circumstances that appear most often in the dynamics literature---it is equivalent to a quasicontinuous function that has an invariant measure.


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Annalisa Crannell. Marc Frantz. Michelle LeMasurier. "Closed relations and equivalence classes of quasicontinuous functions.." Real Anal. Exchange 31 (2) 409 - 423, 2005/2006.


Published: 2005/2006
First available in Project Euclid: 10 July 2007

zbMATH: 1110.54005
MathSciNet: MR2265783

Primary: 54C08 , 54H20‎

Keywords: closed relations , measure , Quasicontinuity , quasicontinuous functions

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 2 • 2005/2006
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