Definitions

Comparability

Comparability

[kom-per-uh-buhl or, sometimes, kuhm-pair-]
In mathematics, two elements x and y of a set partially ordered by a relation ≤ are said to be comparable if and only if xy or yx, or in terms of the strict version of the partial order, if and only if x < y or y < x or y = x. For example, two sets are comparable with respect to inclusion if and only if one is a subset of the other.

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).

See also comparison.

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