ON THE BANACH MAPPING THEOREM AND A RELATED CONJECTURE

Ming Chia Li*

*此作品的通信作者

研究成果: Article同行評審

摘要

We extend, using an elementary method, results of Banach (1924), Fan (1952), and Sanders (1961), which concern a finite collection { fi : Ai → Ai+1}in=1 of mappings with An+1 = A1 which is decomposable as fi(Bi) = Ai+1 \ Bi+1, where Bi ⊆ Ai for all i and Bn+1 = B1. Our theorem determines when such a collection is decomposable. We also show that such a set B1 is unique up to an addition of a certain set, which was conjectured by Sanders.

原文English
頁(從 - 到)183-187
頁數5
期刊Rocky Mountain Journal of Mathematics
52
發行號1
DOIs
出版狀態Published - 2月 2022

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