Determinability of topological spaces by the semigroup of continuous binary relations

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 $CR(X)$.