ИСТИНА

How much do we know about the structure of topological spaces X which can be represented as the union of a not too large collection of subspaces with some nice property? In particular, finite unions of spaces with the weight ≤ τ, finite unions of spaces with a point-countable base, and finite unions of metrizable spaces are especially interesting and deserve to be studied further. We apply the developed approach to the study of remainders of topological groups. Some new theorems on cardinal invariants of remainders of topological groups (including addition theorems for remainders and a criterion of metrizability of topological groups in terms of remainders)) are given.