Abstract
We consider determinability of a topological space \(X\) by a new derived algebraic object, the semigroup \(CR(X)\) of all continuous binary relations on \(X\) with the operation of composition of binary relations, and obtain results on the determinability of a \(T_1\) -space by the semigroup \(CR(X)\) and of an arbitrary topological space \(X\) by an algebraic system related to \(CR(X)\) . We prove that any finite topological space \(X\) is absolutely determined by its semigroup \(CR(X)\) .
