Generalized Alexandroff–Urysohn squares and a characterization of the fixed point property

Given a Hausdorff continuum X, we introduce a topology on X × X that yields a Hausdorff continuum. We call the resulting space the Alexandroff–Urysohn square of X and prove that X has the fixed point property if and only if the Alexandroff–Urysohn square of X has the fixed point property.

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Bibliographic Details
Published in:Topology and its applications 2010-04, Vol.157 (6), p.997-1001
Main Authors: Hagopian, C.L., Marsh, M.M.
Format: Article
Language:English
Subjects:
Fixed point property
Hausdorff continuum
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Summary:Given a Hausdorff continuum X, we introduce a topology on X × X that yields a Hausdorff continuum. We call the resulting space the Alexandroff–Urysohn square of X and prove that X has the fixed point property if and only if the Alexandroff–Urysohn square of X has the fixed point property.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2009.12.015