Singularities of meager composants and filament composants

摘要

Suppose Y is a continuum and X is the union of all nowhere dense subcontinua of Y which contain a given point. Suppose further that there exists y is an element of Y such that every connected subset of X limiting to y is dense in X. And, suppose X is dense in Y. We prove X boolean OR {y} is indecomposable for every y is an element of Y. We then prove X is homeomorphic to a composant of an indecomposable continuum, even though Y may be decomposable. An example establishing the latter was given by Christopher Mouron and Norberto Ordofiez in 2016. If Y is chainable or, more generally, an inverse limit of mutually homeomorphic topological graphs, then Y is necessarily indecomposable. Similar results for homogeneous continua are linked to a 2007 question of Janusz Prajs and Keith Whittington. (C) 2019 Elsevier B.V. All rights reserved.