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Monotone decompositions of continua not separated by any subcontinua

1974
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Transactions of the American Mathematical Society
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Let M be a compact, metric continuum that is separated by no subcontinuum. If such a continuum has a monotone, upper semicontinuous decomposition, the elements of which have void interior and for which the quotient space is a simple closed curve, then it is said to be of type A'. It is proved that a bounded plane continuum is of type A' if and only if M contains no indecomposable subcontinuum with nonvoid interior. In E} this condition is not sufficient and an example is given to illustrate

doi:10.1090/s0002-9947-1974-0341438-x
fatcat:qquttlp4ojhmriyouzzovtqcl4