Purpose. To solve problems: Banach on the existence of a metric separable almost strongly zero-dimensional space X of dimension dim(X)>0; obtaining the most general result on Konamioka compacta, which generalizes Bouziad’s results on the Konamioka compacta of Valdivia; Lindenstrauss and Pelczynski that the infinite-dimensional complementary space of L1 is isomorphic to either L1 or l1.
Application area. Education, basic scientific research
Advantages. Application of previously developed methods (coordinate method, lifting method, embedding method in R-trees) to the study of new objects (subspaces of products of linearly ordered spaces, reflections of the first Beer class, ASZD spaces); the need to create new techniques for studying deformations of Beer maps or studying the properties of ASZD spaces; the need to identify features of the application of the operator scheduling theorem on the space L1 in the case of projectors.
Description. Application of topological methods to solving problems of functional and complex analysis, general and algebraic topology, relating to operators on the space of integration functions, operators on the space of analytic functions, as well as the properties of separation of continuous reflections and their analogues, Beer’s classification with him issues of dimension theory.