Universal objects and associations between classes of Banach spaces and   classes of compact spaces
  In the context of classical associations between classes of Banach spaces and classes of compact Hausdorff spaces we survey known results and open questions concerning the existence and nonexistence of universal Banach spaces and of universal compact spaces in various classes. This gives quite a complex network of interrelations which quite often depend on additional set-theoretic assumptions. 
Piotr Koszmider
math.FA math.GN math.LO