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2008/2009 Almost Continuous Multi-Maps and M-Retracts
Harvey Rosen
Real Anal. Exchange 34(2): 471-482 (2008/2009).


We give results about almost continuous multi-valued functions and a characterization of compact almost continuous $M$-retracts of the Hilbert cube $Q$, where almost continuity is in the sense of Stallings instead of Husain. For instance, each connectivity or almost continuous point to closed-set valued multi-function $f:I \to I$, where $I=[0\,,\,1]$, has a fixed point; i.e., a point $x\in I$ such that $x\in f(x)$. When $Y$ is a compact subset of $Q$, a sufficient condition is given for a continuous multifunction $r:Y\to Y$, with $x\in r(x)$ $\forall x\in Y$, to have an almost continuous multi-valued extension $r:Q \to Y$.


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Harvey Rosen. "Almost Continuous Multi-Maps and M-Retracts." Real Anal. Exchange 34 (2) 471 - 482, 2008/2009.


Published: 2008/2009
First available in Project Euclid: 29 October 2009

zbMATH: 1195.54045
MathSciNet: MR2010329

Primary: 26E25 , 54C05 , ‎54C60‎ , 54H25

Keywords: $M$-retracts , almost continuous multi-valued functions , connectivity , continuous , Fixed points

Rights: Copyright © 2008 Michigan State University Press

Vol.34 • No. 2 • 2008/2009
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