Accessibility of countable sets in plane embeddings of arc-like continua

Scientific paper - Original scientific paper

• Author: Ana Anušić
• Author: Logan C. Hoehn
• Author's institution: University of Zagreb; Faculty of Electrical Engineering and Computing; (Department of Applied Mathematics)
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics; Geometry and Topology

Abstract (english)

We consider the problem of finding embeddings of arc-like continua in the plane for which each point in a given subset is accessible. We establish that, under certain conditions on an inverse system of arcs, there exists a plane embedding of the inverse limit for which each point of a given countable set is accessible. As an application, we show that for any Knaster continuum K, and any countable collection C of composants of K, there exists a plane embedding of K in which every point in the... More union of the composants in C is accessible. We also exhibit new embeddings of the Knaster bucket-handle continuum in the plane which are attractors of plane homeomorphisms, and for which the restriction of the plane homeomorphism to the attractor is conjugate to a power of the standard shift map.
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• Keywords (english): Plane embeddings; accessible point; arc-like continuum; Knaster continuum; attractor
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Submitted version
• Journal title: Journal of the London Mathematical Society
• Numbering: vol. 111, no. 3, e70103
• p-ISSN: 0024-6107
• e-ISSN: 1469-7750
• DOI: https://doi.org/10.1112/jlms.70103
• URN:NBN: urn:nbn:hr:168:652532
• Online first: 2025-03
• Document URL: https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70103
• Type of resource: Text
• Access conditions: Open access
• Created on: 2025-03-27 12:08:19