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Mutually Aposyndetic Decomposition of Homogeneous Continua

Published:2009-12-04
Printed: Feb 2010
• Janusz R. Prajs,
California State University Sacramento
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Abstract

A new decomposition, the \emph{mutually aposyndetic decomposition} of homogeneous continua into closed, homogeneous sets is introduced. This decomposition is respected by homeomorphisms and topologically unique. Its quotient is a mutually aposyndetic homogeneous continuum, and in all known examples, as well as in some general cases, the members of the decomposition are semi-indecomposable continua. As applications, we show that hereditarily decomposable homogeneous continua and path connected homogeneous continua are mutually aposyndetic. A class of new examples of homogeneous continua is defined. The mutually aposyndetic decomposition of each of these continua is non-trivial and different from Jones' aposyndetic decomposition.
 Keywords: ample, aposyndetic, continuum, decomposition, filament, homogeneous
 MSC Classifications: 54F15 - Continua and generalizations 54B15 - Quotient spaces, decompositions