Białystok Scott - Continuous Functions 1 Adam Grabowski University of Białystok

Let S be a non empty set and let a, b be elements of S. The functor a, b, ... yields a function from N into S and is defined by the condition (Def. 1). (Def. 1) Let i be a natural number. Then (i) if there exists a natural number k such that i = 2 ·k, then (a, b, ...)(i) = a, and (ii) if it is not true that there exists a natural number k such that i = 2 ·k, then (a, b, ...)(i) = b. We now state two propositions: (1) Let S, T be non empty reflexive relational structures, f be a map from S into T , and P be a lower subset of T . If f is monotone, then f(P ) is lower. (2) Let S, T be non empty reflexive relational structures, f be a map from S into T , and P be an upper subset of T . If f is monotone, then f(P ) is upper.