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2000/2001 Porosity in Spaces of Darboux-Like Functions
Harvey Rosen
Real Anal. Exchange 26(1): 195-200 (2000/2001).


It is known that the six Darboux-like function spaces of continuous, extendable, almost continuous, connectivity, Darboux, and peripherally continuous functions $f\:R\to \R$, with the metric of uniform convergence, form a strictly increasing chain of subspaces. We denote these spaces by \C, \E, \AC, \Conn, \D, and \PC, respectively. We show that C and D are porous and AC and Conn are not porous in their successive spaces of this chain.


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Harvey Rosen. "Porosity in Spaces of Darboux-Like Functions." Real Anal. Exchange 26 (1) 195 - 200, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 2 January 2009

zbMATH: 1035.26004
MathSciNet: MR1825503

Primary: 26A15 , 54C08 , 54C35‎

Keywords: almost continuous , connectivity , Darboux , extendable , peripherally continuous functions , porosity , spaces of continuous

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 1 • 2000/2001
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