KKM implies Hahn-Banach

Yıl 2019, Cilt: 2 Sayı: 1, 7 - 17, 30.04.2019

Sehie Park

Öz

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 (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.

Anahtar Kelimeler

KKM theory, KKM theorem, Brouwer fixed point theorem, Hahn-Banach theorem

Kaynakça

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