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A remark on fixed points of functors in topological categories

✍ Scribed by JirÍ Adámek

Publisher
Springer
Year
1996
Tongue
English
Weight
263 KB
Volume
4
Category
Article
ISSN
0927-2852

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✦ Synopsis

For a topological category/C over Set we prove that if a functor T: /C --+/C has a fixed cardinal a (i.e./or each object K with card (UK) = a we have card (UTK) <~ c~), then T has a least fixed point, and if T has a successive pair of fixed cardinals a and a +, then T has a greatest fixed point. This extends results of Ad~lmek and Koubek.

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