VITALY VITALIEVICH FEDORCHUK

Head of Department of General Topology and Geometry, Professor

Born on November 1, 1942

Graduated from Moscow State University in 1964

Candidate of Sciences (Ph.D.) in Physics and Mathematics since 1968

In 1977 defended the thesis `Spectra of topological spaces and some problems in General Topology' and was conferred the `Doctor of Sciences' (Dr.-Prof.) degree

Was awarded Professor academic rank in 1983

Author of more than 90 scientific works

Has advanced 26 disciples to the `Candidate of Sciences' (Ph.D.) degree, three of them have got the `Doctor of Sciences' (Dr.-Prof.) degree

V.V.Fedorchuk's first large-scale series of results is related to uniform topology. He introduced the notion of a $\theta$-proximity on a Hausdorff space; within the theory of $\theta$-proximity spaces he concatenated Yu.M.Smirnov's theory of compactifications of proximity spaces and V.I.Ponomarev's theory of absolutes, and also solved A.N.Tychonoff's problem on proximity description of all $H$-closed extension of a given topological space.

V.V.Fedorchuk has made a significant contribution to dimension theory, mainly by constructing remarkable examples. First, this was the construction of a first countable compactum $X$ with non-coinciding Lebesgue and small inductive dimensions and having no partitions with dimension less than $dim\; X$. This showed that the axiomatics for the dimension of metric compact spaces, which had been established by P.S.Alexandroff in 1932, could not be extended to the case of arbitrary compacta. Further V.V.Fedorchuk constructed compacta without intermediate dimensions, hereditarily normal compacta with non-monotone dimensions dim and Ind (under additional set-theoretic assumptions), an example of a zero-dimensional perfect map from a one-dimensional perfectly normal countably compact space onto a zero-dimensional space (assuming Jensen's principle). In the class of compacta, Fedorchuk gave a negative solution to Alexandroff's problem on the coincidence of weak infinite-dimensionality and countable-dimensionality.

One of the most significant scientific accomplishments of V.V.Fedorchuk is developing the method of fully closed maps and expandable spectra which permitted him to solve a series of old and complicated problems in General Topology (first of all in dimension theory and the theory of cardinal invariants). Compacta constructed by using this method are called Fedorchuk's compacta now throughout the World. An hereditarily separable compactum of hyper-continual cardinality constructed by V.V.Fedorchuk under Jensen's principle, should also be mentioned. The methods developed by V.V.Fedorchuk essentially provided tools for his disciples and other topologists from Moscow school to solve some other difficult problems. The result of V.M.Ulyanov who solved the main problem of the theory of compactifications by Fedorchuk's method worth being mentioned here. Recently V.V.Fedorchuk and his disciples study mostly infinite-dimensional topology and the theory of covariant functors (especially the functor of probability measures). In this aspect V.V.Fedorchuk's scientific school holds a leading position.

The following are among recent prominent results of V.V.Fedorchuk: the construction (under the continuum hypothesis) of a differentiable $n$-manifold $M^n^$, $n\ge 4$, with non-coinciding dimensions ind, dim and Ind; the theorem claiming that an arbitrary normal functor acts on Souslin number of spaces in the same way as raising to its degree (in the case of a functor of infinite degree --- as the countable power of a space) --- this is a joint result with S.Todorcevic.