Nonseparable complete Erdös spaces and submeasures on uncountable cardinals
by
Kirsten Valkenburg
Vrije Universiteit Amsterdam, the Netherlands
Coauthors: Jan J. Dijkstra and Dave Visser

Among the applications of their topological characterization of complete Erdös space, E_c, Dijkstra and van Mill state one about copies of E_c in Banach spaces l^p and one concerning Polishable F_s-ideals on w. Inspired by our previous success in lifting the first result to so-called nonseparable complete Erdös spaces in l^p_k for arbitrary infinite cardinal numbers k, we now attempt to generalize the second. We find a partial generalization for submeasures on k and related ideals. For a certain subclass, we state a full generalization, which links the ideals with nonseparable complete Erdös spaces.

Date received: April 17, 2008