Research
My research interests are centered on the use of convergence spaces in Topology and Analysis. A large part of my research has been devoted to the convergence-theoretic approach to topological problems. As this approach matured, it resulted in the book Convergence Foundations of Topology.
Naturally, I am also interested in General and Set-Theoretic Topology, whether convergence structures are involved or not.
I am particularly interested in problems of stability under product, and problems involving Function Spaces and Hyperspaces (which are all areas where applications of convergence structures are abundant).
A broader interest of mine is the use of abstract structures generalizing topological structures, as presented in the book Beyond Topology that I edited. As a result, while my knowledge of abstract category theory is not very deep, I am interested in, and often use, Categorical Topology.
I invite you to take a look at my published and in progress work linked in the drop-down menu.
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