Comparability
From Wikipedia, the free encyclopedia
In mathematics, comparability is the condition of two objects which are related by some relation. For example, in a partially ordered set, two elements x and y are said to be comparable if and only if x < y or y < x; in a set, two subsets are comparable with respect to set inclusion if and only if one is a subset of the other; and in a classification of mathematical objects such as topological spaces, two criteria are said to be comparable when the objects that obey one criterion constitute a subset (or subclass) of the objects that obey the other one (so the T1 and T2 axioms are comparable, while the T1 axiom and the sobriety axiom are not).
