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Mutually Aposyndetic Decomposition of Homogeneous Continua

Dedicated to Charles L. Hagopian and James T. Rogers

Part of: Special properties Basic constructions

Published online by Cambridge University Press:  20 November 2018

Janusz R. Prajs
Janusz R. Prajs*
Affiliation:
California State University Sacramento, Department of Mathematics and Statistics, 6000 J Street, Sacramento, CA 95819, USA, e-mail: prajs@csus.edu
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Abstract

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A new decomposition, the 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

ampleaposyndeticcontinuumdecompositionfilamenthomogeneous

MSC classification

Secondary: 54F15: Continua and generalizations 54B15: Quotient spaces, decompositions
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 1 , 01 February 2010 , pp. 182 - 201
Copyright
Copyright © Canadian Mathematical Society 2010

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