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

MONOTONE IMAGES OF WSETS AND HEREDITARILY WEAKLY CONFLUENT IMAGES OF CONTINUAJonathan Hatch and C. V. StanojevicDepartment 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 654090020, USAAbstract: 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: Wsets; class W; monotone maps; HWC maps Classification (MSC2000): 54F15; 54C50 Full text of the article: (for faster download, first choose a mirror)
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© 2004 Mathematical Institute of the Serbian Academy of Science and Arts
