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An Increasing Homeomorphism of the open unit Interval with Uncountably many Conjugacy Classes of Decreasing Functional Square Roots
Author(s) -
Mestel B. D.
Publication year - 1986
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/18.3.306
Subject(s) - mathematics , homeomorphism (graph theory) , unit interval , conjugacy class , unit square , interval (graph theory) , square (algebra) , unit (ring theory) , combinatorics , topological conjugacy , discrete mathematics , pure mathematics , geometry , mathematics education
P. J. McCarthy and W. Stephenson have asked whether there exists an increasing homeomorphism β of the open unit interval with uncountably many conjugacy classes of decreasing continuous functional square roots. In this paper, we construct an example of a homeomorphism β with this property.