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Some nowhere equicontinuous homeomorphisms


Author: Ki Woong Kim
Journal: Proc. Amer. Math. Soc. 60 (1976), 304-308
MSC: Primary 57E20; Secondary 54H20
DOI: https://doi.org/10.1090/S0002-9939-1976-0423391-0
MathSciNet review: 0423391
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Abstract: It is shown that a nowhere equicontinuous homeomorphism can be defined on a compact polyhedron X if and only if X does not have cell decomposition which contains a principal 1-cell. It is also shown that for each locally connected contractible continuum C in the plane, there is a nowhere equicontinuous homeomorphism $ {h_c}$ on a disk in the plane such that the fixed point set of $ {h_c}$ is C.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0423391-0
Keywords: Equicontinuous homeomorphism, irregular set, dense orbit, principal ncell, strong cellularity
Article copyright: © Copyright 1976 American Mathematical Society

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