KKM implies Hahn-Banach

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Results in Nonlinear Analysis
Volume:2 Issue:1
KKM implies Hahn-Banach

KKM implies Hahn-Banach

Authors : Sehie PARK

Pages : 7-17

View : 18 | Download : 7

Publication Date : 2019-04-30

Article Type : Research Paper

Abstract :Our title means that the Knster-Kuratowski-Mazurkiewitz theorem in 1929 implies the Hahn-Banach theorem. This theorem originated from Hahn in 1926 and Banach in 1929 is of basic importance in the analysis of problems concerning the existence of continuous linear functionals. Its consequences and applications cover hundreds of papers. For a long period, some authors studied the relation of results of the Hahn-Banach theorem and the Brouwer fixed point theorem in 1910 insert ignore into journalissuearticles values(equivalently, the KKM theorem in 1929);. In the present article, we recall some history of such study, and show that the Hahn-Banach theorem can be derived from the KKM theorem and not conversely. Consequently, all consequences and applications of the Hahn-Banach theorem belong to a partial realm of the KKM theory.
Keywords : KKM theory, KKM theorem, Brouwer fixed point theorem, Hahn Banach theorem

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