Mutually Aposyndetic Decomposition of Homogeneous Continua

Prajs, Janusz R.

Canadian journal of mathematics, Tome 62 (2010) no. 1, pp. 182-201

Résumé

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.

Détail

DOI : 10.4153/CJM-2010-010-4

Mots-clés : ample, aposyndetic, continuum, decomposition, filament, homogeneous

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