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

This paper studies maximality and totality of stable functions in the category of stable bifinite domains. We present three main results as follows,(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.