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Hereditarily weakly confluent maps and a characterization of Class HW

✍ Scribed by E.E. Grace; E.J. Vought

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 90 KB
Volume: 100
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(98)00093-5

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✦ Synopsis

First it is proved that the image of any hereditarily unicoherent continuum under a hereditarily weakly confluent map is also hereditarily unicoherent. This answers a question raised in 1979 by T. Maćkowiak. Second, a characterization is established for Class HW, i.e., for the class of all continua Y such that each mapping from a continuum onto Y is hereditarily weakly confluent. That characterization is used to prove J.F. Davis' theorem that atriodic, acyclic curves are in Class HW.