Work

Circularly chainable continua that annularly inscribe squares

Year: 2025

Type: article

Abstract: Let A denote the annulus { x ∈ R 2 : 1 ≤ | | x | | ≤ 1 + 2 } . In this paper we prove that if X is a circularly chainable continuum essentially embedded in A , then X contains the four vertices of an Euclidean square of side length at least 2 . Furthermore, let us say that a plane continuum X satisfies the property of annular inscription in A if whenever X is essentially embedded in A , the image of such embedding admits an inscribed square of side length at least 2 . We show that every circularly chainable, not chainable plane continuum satisfies the property of annular inscription in A and, moreover, that the property of annular inscription in A is generic among continua that separate the plane.

Source: Topology and its Applications

DOI: 10.1016/j.topol.2025.109379

Authors: Ulises Morales-Fuentes, Cristina Villanueva-Segovia

Institutions: Universidad Autónoma del Estado de Morelos, Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,920

Funders: Consejo Nacional de Ciencia y Tecnología, Universidad Nacional Autónoma de México