# codomain

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An initial object in a category C is an object for which every other object of C is a codomain of a unique morphism with the initial object as a domain.

In this diagram the classes are represented by rectangles and the relations by arrows (domain towards codomain) labelled by the name of the relation.

(iii) [F.sub.2] (R), [F.sub.3] (R), [G.sub.2] (R), and [G.sub.3] (R) to be R, where R is considered with the appropriate domain and codomain.

However, it presents a drawback highlighted in [25] and related to the fact that its codomain is the limited interval (0, [pi]/2); thus its normalizing effect may turn out to be meagre, as already pointed out in some studies where it has been used for estimating the reliability of stress-strength models [19, 25, 26].

The vectors RL and [R.sup.[??]] L are particular vectors characterizing, respectively, the domain and codomain of R.

Thus, an error criterion ci is an onto-function with domain in I, and codomain in M:

Taking every other value of i ensures that the complement of the codomain is infinite: we will need this in the next step.

K-metric and K-normed spaces were introduced in the mid-20th century (see [2, 16, 24, 26]) by using an ordered Banach space instead of the set of real numbers, as the codomain for a metric.

Observe that (0,1] is a semi-open set in the codomain that contains f(1) = 1.

Equivalently, f is a submersion if its differential has constant rank equal to the dimension of the codomain of f .

The function f(x) is nondecreasing and piecewise linear, and its codomain is [[l.sub.min], [l.sub.max]].

We thus conclude that the codomain of [member of] of Definition 4.4 can be extended to the family [[Delta].sup.+.sub.1] of all nondecreasing functions [member of] : [0, +[infinity]] [right arrow] [0, 1] such that F(0) = 0 and E([infinity]) = 1.

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