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Proceedings of the American Mathematical Society

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

 
 

 

A note on attractors for compact sets


Author: J. L. Solomon
Journal: Proc. Amer. Math. Soc. 65 (1977), 293-296
MSC: Primary 47H99; Secondary 54H25
DOI: https://doi.org/10.1090/S0002-9939-1977-0637100-4
MathSciNet review: 0637100
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Abstract: Let G be a closed convex subset of a Banach space $ X,f:G \to G$ a continuous map and $ M \subset G$ an attractor for compact sets under f. It is shown that if M is not connected, then M has a unique invariant component which is an attractor for points; moreover, for each x in G, the set of subsequential limit points of x under f is a subset of this unique invariant component.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0637100-4
Keywords: Banach space, attractor for compact sets, component, connected
Article copyright: © Copyright 1977 American Mathematical Society

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