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Proceedings of the American Mathematical Society

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

 

 

Fixed point sets of $ {\rm LC}\sp{\infty }$, $ C\sp{\infty }$ continua


Author: John R. Martin
Journal: Proc. Amer. Math. Soc. 81 (1981), 325-328
MSC: Primary 54F20; Secondary 54H25
DOI: https://doi.org/10.1090/S0002-9939-1981-0593482-4
MathSciNet review: 593482
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Abstract: A space $ X$ is said to have the complete invariance property (CIP) if every nonempty closed subset of $ X$ is the fixed point set of some self-map of $ X$. An example is given to show that there is an $ L{C^\infty }$, $ {C^\infty }$ continuum $ X$ which does not have CIP. Moreover, $ X$ is a wedge of two $ L{C^\infty }$, $ {C^\infty }$ continua each of which has CIP.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0593482-4
Keywords: $ L{C^\infty }$, $ {C^\infty }$ continuum, fixed point set, wedge, complete invariance property
Article copyright: © Copyright 1981 American Mathematical Society