adj. 1. (of a topological space ) containing a countable dense subset. Every compact metric space or second-countable space is separable, as is Euclidean space since it contains the rational n-tuples, which are countable and dense. 2. (of a function) able to be written so that variables are separated, additively or multiplicatively, as, for example, if
f(x, y, z) = f₁(x) + f₂(y) + f₃(z).
This is very useful in computational optimization since minimization can be performed term by term. 3. (of a polynomial) such that the irreducible factors have no repeated roots. 4. (of an extension field) such that every element in the extension has a minimum polynomial that is separable. Every extension of a field of characteristic zero is separable. 5. (of a first order ordinary differential equation) such that it can be written in the form y' = g(y)h(t) and hence can be integrated directly to yield a solution of the formSee separation of variables.