Eduard Helly

Eduard Helly (1884, Vienna – 1943, Chicago) was a mathematician and the eponym of Helly's theorem, Helly families, Helly's selection theorem, Helly metric, and the Helly–Bray theorem. In 1912, Helly published a proof of Hahn–Banach theorem, 15 years before Hahn and Banach discovered it independently. Helly only proved the special case of the Hahn-Banach theorem for continuous functions over [a,b]. The space C[a,b] is infinite dimensional, and the general proof for the infinite dimensional case requires the Axiom of choice or something equivalent, which didn't exist in 1912, so how did Helly prove it? Was his proof even correct? The answer is that C[a,b] is a particular concrete example and he constructed a particular extension for that example. The essence of the Hahn-Banach theorem lies in its generality, which does require the axiom of choice.

 As a prisoner of war in a Russian camp at Nikolsk-Ussuriysk in Siberia, Helly wrote important contributions on functional analysis[1].

Sources

  1. ^ Günter M. Ziegler: Wo die Mathematik entsteht (Where mathematics originate), in: Die Zeit, weekly newspaper, Hamburg, no. 16, 15 April 2010, p. 40

External links