A new class of Corson compacts
by
Arkady Leiderman
Ben-Gurion University, Beer-Sheva, ISRAEL

It is known a number of Corson compacts which do not belong to the class of Gul'ko compacts. Motivated by the nature of these examples we give definition of some new subclass of Corson compacts. Every such Corson compact admits a special embedding into \Sigma- product of the real lines. For any \omega₁ - tree one can construct an adequate Corson compact. We consider several examples of trees such that its adequate compacts distinguish defined classes. A question whether every member of introduced class contains a dense metrizable subspace is studied. We present a new definition of the class of Banach spaces which is between weakly countably determined and weakly Lindelof determined Banach spaces.

Date received: June 24, 2000