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

Znanstveni rad - Izvorni znanstveni rad

• Autor: Ana Anušić
• Autor: Logan C. Hoehn
• Autorova ustanova: Sveučilište u Zagrebu; Fakultet elektrotehnike i računarstva; (Zavod za primijenjenu matematiku)
• Znanstveno / umjetničko područje, polje i grana: PRIRODNE ZNANOSTI; Matematika; Geometrija i topologija

Sažetak (engleski)

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... Više 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.
. Sakrij dio sažetka

• Ključne riječi (engleski): Plane embeddings; accessible point; arc-like continuum; Knaster continuum; attractor
• Jezik: engleski
• Vrsta publikacije: Znanstveni rad - Izvorni znanstveni rad
• Status objave: Objavljen
• Vrsta recenzije: Recenziran - međunarodna recenzija
• Verzija publikacije: Rukopis poslan na recenzijski postupak (preprint)
• Naslov časopisa: Journal of the London Mathematical Society
• Brojčani podaci: vol. 111, br. 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
• Datum objave elektroničkog izdanja: 2025-03
• URL dokumenta: https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70103
• Vrsta resursa: Tekst
• Prava pristupa: Otvoreni pristup
• Datum i vrijeme pohrane: 2025-03-27 12:08:19