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1999/2000 Simultaneous Extension Operators for the Density Topology
Jan Kolář
Real Anal. Exchange 25(1): 223-230 (1999/2000).


Given a set $M\subset\R$ of Lebesgue measure zero, let $\B_1\vert_M$ be the set of all restrictions to $M$ of bounded Baire one functions on $\R$ and $\A$ the set of all bounded approximately continuous functions on $\R$. We discuss the existence of simultaneous extension operators for $\B_1\vert_M$ and $\A$. We show that there exists a~positive linear operator $L\colon\B_1\vert_M\to\A$ such that $L(g)\vert_M=g$ for all $g\in\B_1\vert_M$, if and only if $M$ is a~scattered set and this is the case if and only if there exists a~continuous linear operator $L_1\colon\B_1\vert_M\to\A$ with the same property. Also, we show that there exist non-regular continuous linear operators $T_1\colon \ell_\infty \to \A$ and $T_2\colon\A\to\A$.


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Jan Kolář. "Simultaneous Extension Operators for the Density Topology." Real Anal. Exchange 25 (1) 223 - 230, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 5 January 2009

zbMATH: 1015.54006
MathSciNet: MR1758003

Primary: ‎46E15 , 54A10 , 54C20

Keywords: approximately continuous functions , density topology , simultaneous extension operator

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 1 • 1999/2000
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