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$ \lambda $ connectivity and mappings onto a chainable indecomposable continuum


Author: Charles L. Hagopian
Journal: Proc. Amer. Math. Soc. 45 (1974), 132-136
MSC: Primary 54F20
DOI: https://doi.org/10.1090/S0002-9939-1974-0341434-8
MathSciNet review: 0341434
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Abstract: A continuum (i.e., a compact connected nondegenerate metric space) $ M$ is said to be $ \lambda $ connected if any two of its points can be joined by a hereditarily decomposable continuum in $ M$. Here we prove that a plane continuum is $ \lambda $ connected if and only if it cannot be mapped continuously onto Knaster's chainable indecomposable continuum with one endpoint. Recent results involving aposyndesis and decompositions to a simple closed curve are extended to $ \lambda $ connected continua.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0341434-8
Keywords: Hereditarily decomposable continua, $ \lambda $ connected continua, Jones' function $ K$, arcwise connectivity, aposyndesis, decompositions to a simple closed curve, mappings onto an indecomposable continuum
Article copyright: © Copyright 1974 American Mathematical Society

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