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

 

Outlet points and homogeneous continua


Authors: Paweł Krupski and Janusz R. Prajs
Journal: Trans. Amer. Math. Soc. 318 (1990), 123-141
MSC: Primary 54F20; Secondary 54C10, 54F50, 54F55
MathSciNet review: 937246
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Abstract: (1) A proof is presented for Bing's conjecture that homogeneous, treelike continua are hereditarily indecomposable. As a consequence, each homogeneous curve admits the continuous decomposition into the maximal terminal, homeomorphic, homogeneous, hereditarily indecomposable, treelike subcontinua. (2) A homogeneous, hereditarily unicoherent continuum contains either an arc or arbitrarily small, nondegenerate, indecomposable subcontinua. (3) A treelike continuum with property $ K$ which is homogeneous with respect to confluent light mappings contains no two nondegenerate subcontinua with the one-point intersection.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0937246-8
PII: S 0002-9947(1990)0937246-8
Keywords: Homogeneous continuum, treelike continuum, indecomposable continuum, terminal continuum, outlet point, Effros theorem, property $ K$, confluent light mapping
Article copyright: © Copyright 1990 American Mathematical Society