Article ID Journal Published Year Pages File Type
4658764 Topology and its Applications 2014 9 Pages PDF
Abstract
In this paper we extend the study of shore points to every continuum and we prove that every continuum has at least two shore points. This result generalizes an important theorem in Continuum Theory: Every continuum has at leasts two non-cut points. We show that every point of irreducibility is a shore point, and we give some conditions under which a shore point is a point of irreducibility. Also, we characterize uniquely irreducible continua, an arc and a simple closed curve using shore points. Finally, we show that the union of shore points in a uniquely irreducible continua is a shore set.
Keywords
Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology
Authors
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