Using notions and approaches introduced by us (by application of which we have already solved the
problem having over 30 years history and obtained many results) and methods of set theory,
combinatorial geometry, convex analysis and other branches of mathematics, we will study the following
problems:
● Geometrical realizations of general (abstract) families of sets; geometrical realizations of independent
families of sets and structure of constituents of these families in the Euclidean plane and Euclidean space;
● Different types of decompositions and coverings of subsets of the Euclidean space;
● Combinatorial properties of point sets.

Project members:

• Tengiz Tetunashvili (Principal Investigator)