Shore and Non-Block Points in Hausdorff Continua

2020/07/16 by Daron Anderson, Anderson, Daron
Mathematics · #54F15 (Primary) 54G15 #54G20 (Secondary) #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2007.08423

openalex publication_date 2020/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the shore and non-block points of non-metric continua. We reduce the problem of showing a continuum to have non-block points to that of showing an indecomposable continuum to have non-block points. As a corollary we prove that separable continua have at least two non-block points -- and moreover are irreducible about their set of non-block points.

Related

• The Shore Point Existence Problem is Equivalent to the Non-Block Point Existence Problem
• Continuum Without Non-Block Points
• Indecomposable Continuum with a Strong Non-Cut Point
• Fixed points in non-invariant plane continua
• Connectivity degrees of complements of closed sets in continua