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Shifts on zero-dimensional compact metric spaces

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
159
Issue
16
Identifiers
DOI: 10.1016/j.topol.2012.08.012
Keywords
  • Shift
  • Cantor Set
  • Primitive Shift
  • Scattered Space

Abstract

Abstract It is shown that every compact zero-dimensional metric space X with either no isolated points or infinitely many isolated points has a complex shift. If X is a disjoint union of a compact infinite scattered metric space and the Cantor set then X has a real shift also. If X is a disjoint union of a nonempty finite scattered metric space and the Cantor set then X has no shift.

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