Winter School

Invited speakers

Jesús María Fernández Castillo, Universidad de Extremadura, Badajoz, Spain

Marián Fabian, Czech Academy of Sciences, Praha, Czech Republic

Tamás Keleti, Eötvös Loránd University, Budapest, Hungary

Stevo Todorčević, University of Toronto, Toronto, Canada


Jesús M. F. Castillo: Homological methods in Banach space theory far and beyond

Marián Fabian: Asplund story

We present the theory of Asplund spaces from their beginning in 1968 up to now. We mention properties equivalent to the Asplund property - in particular dentability and the Radon-Nikodym property. We show examples/counterexamples, open questions, applications in renormings, and in variational analysis. We also recall adjacent concepts - weak Asplund spaces, Gâteaux differentiability spaces, Asplund-generated spaces, and topological counterparts: scattered and Radon-Nikodym compact spaces. Related techniques are also presented; in particular separable reductions, rich families, and projectional skeletons.