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Fully closed mappings and their applications. (Russian. English summary) Zbl 1073.54010
Fundam. Prikl. Mat. 9, No. 4, 105-235 (2003); translation in J. Math. Sci., New York 136, No. 5, 4201-4292 (2006).
The paper contains a deep and self-contained review of the results of the author and of his students on fully closed mappings and on their applications. The author gives necessary introductory material, describes in a systematic way fully closed mappings and their interrelations with fiber products, inverse systems and resolvents. The projective properties of fully closed maps, spectral trees, convolutions and involutions are studied. Different applications are provided, at most the applications related to the dimension and cardinal functions. Also a class of homogeneous bicompacts is considered. The survey is worth to be read by any mathematician working in the subject.

54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
54A35 Consistency and independence results in general topology
54F45 Dimension theory in general topology