Abstract
We import into continuum theory the notion of extreme point of a convex set from the theory of topological vector spaces. We explore how extreme points relate to other established types of “edge point” of a continuum; for example we prove that extreme points are always shore points, and that any extreme point is also non-block if the continuum is either decomposable or irreducible (in particular, metrizable).In addition we discuss some continuum-theoretic analogues of the celebrated Krein-Milman theorem.
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