Pseudoradial Spaces: Results and Problems

In this paper it is given a survey of principal results (old and new) concerning the class of pseudoradial spaces. In this class cardinal invariants and their inequalities are considered. The behaviour of pseudoradial spaces under the operations of taking topological products and subspaces are examined and a typical proof is given. A particular attention is dedicated to the so called “small cardinals” in connection with pseudoradiality. Pseudoradiality of 2^{ω 2} is also examined. It is proved that pseudoradiality can be ω¹ productive for spaces of weight at most ω². Finally, several open problems are presented. This work was supported by the National Group “Real Analysis, Measure Theory with Applications to Economy” of the Italian Ministery of Education, University and Research.