EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)
Vol. 74(88), pp. 111–114 (2003)

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MONOTONE IMAGES OF W-SETS AND HEREDITARILY WEAKLY CONFLUENT IMAGES OF CONTINUA

Jonathan Hatch and C. V. Stanojevic

Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA and Department of Mathematics and Statistics, University of Missouri – Rolla, 202 Rolla Building, Rolla, MO 65409-0020, USA

Abstract: A proper subcontinuum $H$ of a continuum $X$ is said to be a $W$-set provided for each continuous surjective function $f$ from a continuum $Y$ onto $X$, there exists a subcontinuum $C$ of $Y$ that maps entirely onto $H$. Hereditarily weakly confluent (HWC) mappings are those with the property that each restriction to a subcontinuum of the domain is weakly confluent. In this paper, we show that the monotone image of a $W$-set is a $W$-set and that there exists a continuum which is not in class $W$ but which is the HWC image of a class $W$ continuum.

Keywords: W-sets; class W; monotone maps; HWC maps

Classification (MSC2000): 54F15; 54C50

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Electronic fulltext finalized on: 21 Dec 2004. This page was last modified: 9 Feb 2005.

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