Research Worker of Department of General Topology and Geometry
Born on February 20, 1944
Candidate of Sciences (Ph.D.) in Physics and Mathematics (1970)
Author of 16 scientific works
V.I.Zaitsev is known as a specialist in the theory of projection spectra. He introduced the general concept of an abstract spectrum and showed that the full limit of any (finite) projection spectrum is a semi-regular (compact) -space, and upper and lower limits are (compact) -spaces. V.I.Zaitsev proved the representation theorem claiming that every finite abstract projection spectrum is equivalent to a spectrum over some directed set of canonical covers of a compact -space. In connection with the theory of projection spectra, V.I.Zaitsev also studied compactifications and some classes of spaces which are close to normal spaces.
In 1967 V.I.Zaitsev proved the theorem characterizing Tychonoff spaces by the existence of a base with special conditions, which became one of `brilliants' in General Topology; this way the problem of finding an internal characterization of Tychonoff spaces apart from the external definition by the aid of functions, was solved.
One of the recent V.I.Zaitsev's results is the extension to maps of well-known Kurosch's theorem on the compactness of full and lower limits of a spectrum of finite -spaces: the limit and the lower limit of an inverse spectrum of closed finite-fold -maps are perfect maps.