Subsequently, I turned my interest to uniform spaces. In particular, I investigated uniform paracompactness. One of my major fields of interest consists in linearly uniformizable spaces (uniform spaces with a linearly ordered basis). I studied topics related to the completeness of the hyperspace of a linearly uniformizable space, equipped with the Hausdorff uniformity, after discovering a gap in the proof of a theorem well-known in the literature. I found a counterexample and characterized the spaces which admit a complete hyperspace. The supercompleteness of exp(k), equipped with the k-product uniformity, relies on set-theoretic assumptions.
In a recent paper, a strengthening of completeness condition lead to prove the existence of a selection for lower semicontinuous multivalued functions. Therefore I turned my attention to problems dealing with the existence of continuous selectors in a non-archimedean space. I proved that such a space admits a continuous selector for the Vietoris topology if and only if it is scattered (or topologically well ordered). Some results about selectors in scattered spaces are related to the existence of measurable cardinals.
Finally I found some results dealing with selectors and orderability. For the main results about these topics, goto abstract 1, abstract 2, abstract 3 in the Topology Atlas.
Part of the above results have been obtained in cooperation with other researchers.
I participated to several international meetings in Topology and collaborated with Italian and foreign researchers.
Together with my colleagues in Padova, I am organizing ITES2007, the «Sixth Italian-Spanish Conference on General Topology and applications».
In 1977 I became assistant professor of mathematical analysis at the Faculty of Science of Padova University. Since 1985, I am associated professor of Mathematical Analysis in the same Faculty.