On topological machines

摘要

A topological machine is a topologized quasi-machine of Ginsburg and is defined by two continuous functions f and gT←g×S→f, the state-transition function and the output function, respectively, where X is a nonvoid T2-space, the state space, S and T are two topological semigroups, the input semigroup and the output semigroup, respectively, such that f(x, s1s2)=f(f(x, s1), s2) and g(x, s1s2)=g(x, s1)g(f (x, s1), s2) for all x ∈ X and all s1, s2 ∈ S. In Section 1 of this paper some results are obtained toward the structure of the output function for a few special classes of machines and, in Section 2, some basic concepts and results of the algebraic theory are extended to the topological case.