Scott - Continuous Functions . Part II 1 Adam Grabowski University of Białystok
نویسنده
چکیده
One can prove the following proposition (1) Let S, T be up-complete Scott top-lattices and M be a subset of SCMaps(S, T ). Then ⊔ SCMaps(S,T ) M is a continuous map from S into T . Let S be a non empty relational structure and let T be a non empty reflexive relational structure. One can check that every map from S into T which is constant is also monotone. Let S be a non empty relational structure, let T be a reflexive non empty relational structure, and let a be an element of the carrier of T . One can check that S 7−→ a is monotone. One can prove the following propositions: (2) Let S be a non empty relational structure and T be a lower-bounded antisymmetric reflexive non empty relational structure. Then ⊥MonMaps(S,T ) = S 7−→ ⊥T . (3) Let S be a non empty relational structure and T be an upperbounded antisymmetric reflexive non empty relational structure. Then ⊤MonMaps(S,T ) = S 7−→ ⊤T .
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