Generalizations of sequentiality and set theoretic assumptions
by
Gino Tironi
University of Trieste

Under this name we consider various generalizations of sequential spaces, the principal beeing the class of pseudoradial spaces. This class was first introduced by H. Herrlich in 1967 and successively fully investigated by Arhangel'ski. Another subclass of pseudoradial spaces considered at the beginning was that of radial spaces, while later on Arhangel'ski introduced the almost-radial spaces. Further subclasses of pseudoradial spaces that were considered successively were the R-monolithic and the semiradial spaces. Related to these classes are also the spaces with the weak Whyburn property. Topological properties of these spaces are strongly related to set theoretic assumptions, as was pointed out unexpectedly in 1990 by Sapirovski. In particular characterizations of various subclasses of pseudoradial spaces are connected to the sequential behaviour of the Cantor cubes 2^\omega₁ and 2^\omega₂. This is one of the subjects that I will investigate.

Date received: June 7, 2003