Monotone decompositions of IUC continua

Collins, W. Dwayne

doi:10.1090/S0002-9947-1984-0732114-6

Monotone decompositions of IUC continua
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by W. Dwayne Collins

Trans. Amer. Math. Soc. 282 (1984), 699-709

DOI: https://doi.org/10.1090/S0002-9947-1984-0732114-6

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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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