On indecomposability of $��X$
| Autor: | Lipham, David Sumner |
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| Rok vydání: | 2017 |
| Předmět: | |
| DOI: | 10.48550/arxiv.1703.06862 |
| Popis: | The following is an open problem in topology: Determine whether the Stone-��ech compactification of a widely-connected space is necessarily an indecomposable continuum. Herein we describe properties of $X$ that are necessary and sufficient in order for $��X$ to be indecomposable. We show that indecomposability and irreducibility are equivalent properties in compactifications of indecomposable separable metric spaces, leading to some equivalent formulations of the open problem. We also construct a widely-connected subset of Euclidean $3$-space which is contained in a composant of each of its compactifications. The example answers a question of Jerzy Mioduszewski. 12 pages, 5 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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