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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some fixed point results for $ UV$ decompositions of compact metric spaces


Authors: John Cobb and William Voxman
Journal: Proc. Amer. Math. Soc. 33 (1972), 156-160
MSC: Primary 54.60
MathSciNet review: 0290340
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Abstract: In this paper the preservation of the fixed point property under UV decompositions is studied. It is shown that if K is an n-dimensional complex with the fixed point property and G is $ U{V^{n - 1}}$ decomposition of K, then K/G also will have the fixed point property. Furthermore, if X is a compact metric space with the fixed point property, and G is a $ U{V^n}$ decomposition of X such that X/G may be embedded in a suitably small Euclidian space, $ {R^m}$, then X/G retains the fixed point property.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0290340-4
PII: S 0002-9939(1972)0290340-4
Keywords: Simplicial complex, compact metric space, UV decomposition, fixed point property
Article copyright: © Copyright 1972 American Mathematical Society