Totally disconnected subsets of chainable continua
David S. Lipham
TL;DR
This paper proves that the endpoint set of a Suslinian chainable continuum must be zero-dimensional at some point, answering a question about the topological structure of such continua and their endpoint sets.
Contribution
It establishes a new topological property of Suslinian chainable continua, specifically regarding the dimensionality of their endpoint sets, and resolves a previously open question.
Findings
Endpoint set of a Suslinian chainable continuum must be zero-dimensional at some point
Cannot be homeomorphic to complete Erdős space
Answers a question posed by Jerzy Krzempek
Abstract
We show that the endpoint set of a Suslinian chainable continuum must be zero-dimensional at some point. In particular, it cannot be homeomorphic to complete Erd\H{o}s space. This answers a question of Jerzy Krzempek.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Homotopy and Cohomology in Algebraic Topology