Professor of Department of General Topology and Geometry
Born on July 14, 1947
Doctor of Sciences (Dr.-Prof.) in Physics and Mathematics (1974)
Professor (1987)
Author of more than 60 scientific works
Has advanced more than 10 disciples to the `Candidate of Sciences' (Ph.D.) degree
First results of V.V.Filippov contributed a lot to reciprocal classification of spaces and maps. The following of his theorems are widely known: perfect maps preserve the class of -spaces and the class of spaces with a point-countable base, a paracompact -space with a point-countable base is metrizable.
The most famous V.V.Filippov's results are the example of a pair of compacta for which the dimension Ind of the product is greater than the sum of their dimensions Ind, and the example of a compactum with non-coinciding dimensions ind and Ind answering an old problem of P.S.Alexandroff. He is also the author of an example of a first countable compactum where the sum theorem for inductive dimensions is not true, and a series of examples (under the continuum hypothesis) of perfectly normal compacta with non-coinciding dimensions dim and ind. V.V.Filippov proposed a simple, purely topological method for extending theorems on dim dimension from metric compacta to much wider classes of spaces, thus a formerly elaborated much more complicated theory based on algebraic methods became irrelevant.
Within the last few years V.V.Filippov studies basic structures of the theory of ordinary differential equations. He developed a robust theory of solution spaces of ordinary differential equations which can be applied to a widest variety of equations with singularities. This theory is actually based on the penetration of general-topological approach into the theory of ordinary differential equations which leads the latter to appreciable harmony and fair generality.