Geodesic
Monotone Images of W-sets and Hereditarily Weakly Confluent Images of Continua
Publications de l'Institut Mathématique, _N_S_74 (2003) no. 88, p. 111 .

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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.
DOI : 10.2298/PIM0374111H
Classification : 54F15 54C50
Keywords: W-sets, class W, monotone maps, HWC maps 
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     author = {Jonathan Hatch and \v{C}aslav V. Stanojevi\'c},
     title = {Monotone {Images} of {W-sets} and {Hereditarily} {Weakly} {Confluent} {Images} of {Continua}},
     journal = {Publications de l'Institut Math\'ematique},
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Jonathan Hatch; Časlav V. Stanojević. Monotone Images of W-sets and Hereditarily Weakly Confluent Images of Continua. Publications de l'Institut Mathématique, _N_S_74 (2003) no. 88, p. 111 . doi : 10.2298/PIM0374111H. http://geodesic.mathdoc.fr/articles/10.2298/PIM0374111H/

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