The aim of this research is to apply the latest results and methods of both combinatorial and axiomatic set-theory to various problems in topology. Experience shows that a large percentage of such problems, though easily formulated, lead to deep set- theoretic questions, and in particular can only be resolved as independence results. I. Juhasz is an expert and actually one of the initiators of research in this borderline area; his cooperation with M. E. Rudin, who is mainly a topologist, and with K. Kunen and A. Miller, who are mainly set-theorists, is expected to yield solutions to several natural problems of topology as well as to clarify their set-theoretic background. These, in turn, may lead to significant contributions to set-theory itself.
