The Nadler-Quinn problem for simplicial inverse systems

2023/11/23 by Andrea Ammerlaan, Ammerlaan, Andrea, Ana Anušić +3
Computer Science · Mathematics · #54C25 #FOS: Mathematics #General Topology (math.GN) #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Primary 54F15 #Secondary 54F50 #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2311.14128

openalex publication_date 2023/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if X is an arc-like continuum which can be represented as an inverse limit of a simplicial inverse system on arcs, then for every point x ∈ X there is a plane embedding of X in which x is accessible. This answers a special case of the Nadler-Quinn question from 1972.

Related

• The Nadler-Quinn problem on accessible points of arc-like continua
• Radial departures and plane embeddings of arc-like continua
• Accessibility of countable sets in plane embeddings of arc-like continua
• Uncountably many planar embeddings of unimodal inverse limit spaces
• An Inverse System of Nonempty Objects with Empty Limit