The hyperspace of closed subsets on the edge of irreducible continua
[EN] For a nonempty nowhere dense closed subset of a continuum $X$, consider the following properties: being a non-weak cut subset, a non-block subset, a weak non-block subset, a shore subset, a non-strong center, and a non-cut subset of X. In this paper, we provide necessary conditions for subsets...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/227663 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/227663 |
| Access Level: | acceso abierto |
| Palabra clave: | Irreducible continuum Non-weak cut set Non-block set Weak non-block set Shore set Non-cut set |
| Sumario: | [EN] For a nonempty nowhere dense closed subset of a continuum $X$, consider the following properties: being a non-weak cut subset, a non-block subset, a weak non-block subset, a shore subset, a non-strong center, and a non-cut subset of X. In this paper, we provide necessary conditions for subsets of an irreducible continuum about a subset to have one of these properties, and we prove that these properties are equivalent for nonempty nowhere dense closed subsets of an irreducible continuum about a finite subset. This result completes the study previously conducted on non-cut points and for subsets on the edge of a continuum by several authors. |
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