Tamás Glavosits

Constructions and Extensions of Free and Controlled Additive Relations

By using several auxiliary results on relations and their intersection convolutions, we give some necessary and sufficient conditions in order that a certain additive partial selection relation Φ of a relation F of one group X to another Y could be extended to a total, additive selection relation Ψ of the relation \(F+\Phi(0)\).

ON THE EXISTENCE OF NONNEGATIVITY DOMAINS OF SUBSETS OF GROUPS

1. A few basic facts on families of sets and subsets of groups A family A of sets is called chained if for any A, B G A we have either A C B or B C A. The family A is called directed if for any A, B 6 A there exists C € A such that A C C and B C C. A subfamily B of a family of sets A is called bounded above in A if there exists A € A such that B C A for all B € B. Moreover, the family A is called inductive if each chained subfamily of A is bounded above in A. 1991 Mathematics Subject Classification: 06P15.