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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Endohomeomorphisms decomposing a space into disjoint copies of a subspace


Author: Liam O’Callaghan
Journal: Proc. Amer. Math. Soc. 72 (1978), 391-396
MSC: Primary 54C45; Secondary 54D35
MathSciNet review: 0500820
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Abstract: The existence (conjectured by R. Levy in a private communication) of a space X and an endohomeomorphism, f, of $ \beta X$, such that $ f[X] = \beta X\backslash X$ is demonstrated. It is shown that if G is one of the topological groups $ {{\mathbf{2}}^\alpha },{{\mathbf{Q}}^\alpha },{{\mathbf{R}}^\alpha }$ or $ {{\mathbf{T}}^\alpha }$, where $ \omega < \alpha $, then G has a dense C-embedded subgroup H and an autohomeomorphism, f, such that G is the union of disjoint sets, $ {A_0}$ and $ {A_1}$, where for $ \{ i,j\} = \{ 0,1\} f[{A_i}] = {A_j}$, and $ {A_i}$ is a union of cosets of H.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0500820-7
Article copyright: © Copyright 1978 American Mathematical Society