Feeding and killing end points in chainable continua

TL;DR

This paper constructs specific chainable continua with end points homeomorphic to any given zero-dimensional, complete separable metric space, answering a previously open question in continuum theory.

Contribution

It introduces a method to realize any zero-dimensional, complete separable metric space as the set of end points of a Suslinian, chainable continuum, solving an open problem.

Findings

Existence of chainable continua with prescribed end point sets

Application of condensation of singularities technique

Addresses an open question in continuum theory

Abstract

Using the classical technique of condensation of singularities, we prove that, for every zero-dimensional, complete separable metric space $G$, there exists a Suslinian, chainable metric continuum whose set of end points is homeomorphic to $G$. This answers a question posed by R. Adikari and W. Lewis in [Houston J. Math. 45 (2019), no. 2, pp. 609--624].