Order unit
An order unit is an element of an ordered vector space which can be used to bound all elements from above.[1] In this way (as seen in the first example below) the order unit generalizes the unit element in the reals.
Definition
For the ordering cone in the vector space
, the element
is an order unit (more precisely an
-order unit) if for every
there exists a
such that
(i.e.
).[2]
Equivalent definition
The order units of an ordering cone are those elements in the algebraic interior of
, i.e. given by
.[2]
Examples
Let be the real numbers and
, then the unit element
is an order unit.
Let and
, then the unit element
is an order unit.
References
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