Truth-table unoids satisfying the Urzyczyn's conditions

In the works of P. Urzyczyn [1-3] were suggested sufficient conditions of truth-table property of unoids, however, these algebraic conditions of Urzyczyn are difficult to be checked in practice and leave no possibilities to build non-trivial examples of truth-table unoids. In this work concepts of locally-given and divided unoids are proposed, and it is proved that divided unoids satisfy the conditions of Urzyczyn. Thus, simply verifiable sufficient conditions are achieved, on the basis of which unoid, including with enough complicated specified connected underlying set, is truth-table.