Maximality and totality of stable functions in the category of stable bifinite domains

Abstract: This paper studies maximality and totality of stable functions in the category of stable bifinite domains. We present three main results as follows, [o] [(1)] every maximum-preserving function is a maximal element in the stable function spaces; [(2)] a maximal stable function f : D → E is maximum-preserving if D is maximum-separable and E is completely separable; and [(3)] a stable bifinite domain D is maximum-separable if and only if for any locally distributive stable bifinite domain E, each maximal stable function f : D → E is maximum-preserving. [Copyright &y& Elsevier]