Algebra Seminar talk
2018-01-12
Luka Ilić
Hahn-Banach implies Banach-Tarski
Abstract:
Contradicting geometric intuition, the Banach-Tarski Paradox may be regarded as
one of the most surprising results of modern mathematics. Its original proof
relies on the Axiom of Choice and as such, was heatedly debated throughout the
20th century. More recently (in 1991) a result by Janusz Pawlikowski was
published, showing that Choice is not needed in full strength to imply the
Banach-Tarski Paradox - he showed that postulating Hahn-Banach suffices.
In my
talk I will introduce the precise statement of the Banach-Tarski Paradox,
present a proof using the Axiom of Choice and additionally present
Pawlikowski’s proof, that Hahn-Banach implies Banach-Tarski.