Singularities of meager composants and filament composants
| Autor: | Lipham, David Sumner |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Topology and its Applications 260 (2019) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.topol.2019.01.010 |
| Popis: | Suppose $Y$ is a continuum, $x\in Y$, and $X$ is the union of all nowhere dense subcontinua of $Y$ containing $x$. Suppose further that there exists $y\in Y$ such that every connected subset of $X$ limiting to $y$ is dense in $X$. And, suppose $X$ is dense in $Y$. We prove $X$ 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 Ordo\~nez in 2016. If $Y$ is chainable or, more generally, an inverse limit of identical topological graphs, then we show $Y$ is indecomposable and $X$ is a composant of $Y$. For homogeneous continua we explore similar problems which are related to a 2007 question of Janusz Prajs and Keith Whittington. Comment: 12 pages, 3 figures |
| Databáze: | arXiv |
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