The fifth lecture in honour of Eduard Cech
Gilles Godefroy
Goemetry of Banach spaces and descriptive set theory
April 1, 2008
In the first years of the twentieth century, Borel reached the concept
of countably additive measure, Lebesgue created his integration theory
and Baire characterized pointwise limits of continuous functions. They
led them, and later on Lusin, Suslin and many others, to investigate
the intrinsic complexity of subsets of metric spaces. Today,this part
of analysis is called descriptive set theory. It has been recently applied
to Banach space theory, and the complexity of natural classes of Banach
spaces has been evaluated and used.
We shall explain how this can be done, and display applications in two
directions: smooth renormings of Banach spaces, existence of universal
spaces.
