Grant: Discovery Grants Program - Individual

My research focuses on general topology and measure theory. Some of the research has a set-theoretic flavor, as both of these areas occasionally require the use of deep set-theoretic techniques. The method of forcing especially, since 1963 when it was developed by Paul Cohen for proving that the Continuum Hypothesis is not decidable on the basis of the usual axioms for set theory, has led to important advances in these areas. One area dealt with in my proposal is measure theory, which is devoted to the study of methods for calculating lengths, areas and volumes and more general notions of a similar type. The problems that concern me have a set-theoretic flavor. Techniques from set theory have been successfully applied to similar problems in the past. Henri Lebesgue proved in 1898 that every real-valued function of two variables which is continuous in each variable separately is a limit of continuous functions. Separate continuity is a property of functions which occurs with sufficient frequency that knowledge of the deeper structure of such functions is potentially useful. Another area dealt with in my proposal is to extend our knowledge of this class.