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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Monotone decompositions of IUC continua


Author: W. Dwayne Collins
Journal: Trans. Amer. Math. Soc. 282 (1984), 699-709
MSC: Primary 54F20; Secondary 54B15
MathSciNet review: 732114
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Abstract: For the class of hereditarily unicoherent metric continua a spectrum of monotone decompositions has been developed by several authors which "improves" the quotient spaces. This spectrum is developed for a broader class of continua, namely continua with property IUC. A metric continuum $ M$ has property IUC provided each proper subcontinuum of $ M$ with interior is unicoherent. One important result which develops is that semiaposyndetic IUC continua are hereditarily arcwise connected. Also the notion of smoothness is studied for IUC continua.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0732114-6
PII: S 0002-9947(1984)0732114-6
Keywords: Hereditarily decomposable, upper semicontinuous decompositions, property IUC, property HIUC, aposyndetic, semiaposyndetic, smooth
Article copyright: © Copyright 1984 American Mathematical Society