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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Cosmic approximate limits and fixed points


Authors: J. Segal and T. Watanabe
Journal: Trans. Amer. Math. Soc. 333 (1992), 1-61
MSC: Primary 55M20; Secondary 54B20, 54B35, 54C56, 54H25
DOI: https://doi.org/10.1090/S0002-9947-1992-1145962-2
MathSciNet review: 1145962
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Abstract: We define a condition for approximate inverse systems which implies that the limit of the system has the fixed point property. Moreover, this condition is categorical in the approximate shape category. We investigate the class of complex projective $ n$-space like continua with respect to the fixed point property by means of this condition. As a further application we show that the hyperspace $ C(X)$ of nonempty subcontinua of an arc-like or circle-like Hausdorff continuum $ X$ has the fixed point property. We also prove that $ {2^X}$ and $ C(X)$ have the fixed point property for any locally connected Hausdorff continuum $ X$.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1145962-2
Keywords: Approximate inverse system, coincidence point, fixed point, hyperspace, cosmic, shape
Article copyright: © Copyright 1992 American Mathematical Society