Physical Sciences and Mathematics Commons^™

Classifications Of Plane Continua, Steven Ray Matthews

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In the course of studying continua in the plane it has been asked if a given continuum has uncountably many disjoint duplications in the plane, and if so, what are the consequences of the existence of such a collection. The object of this paper is to study these problems and to develop some machinery useful in their resolution. In Section I, we review the definition of convergence and homeomorphic convergence of point sets in a metric space S. We then consider the space, π of all continuous functions from a compact metric space P to a separable metric space Q …