Since function f(x) is continuous over the set X and function g(x) is continuous over the codomain of function f(x), function (mathcal {L}) is continuous over the set X. Given (mathcal {L}) is a continuous function that maps a convex set to itself, according to the Brouwer fixed-point theorem, there is a point (x^) such that (mathcal {L}left( x^right) =x^).
Notice, that the codomain of the function l could be easily changed to [ n − 1 ] in place of [ n ] ∪ { 0 }, but we do not do that to discern the 'top' of a simplex from its 'bottom' - see Figure 1.
For instance, n/0 (assuming that the codomain of the function λn.n/0 is extended to permit r to be rational) could be implemented on a computer by a loop (that would never terminate when executed if n≠0) which would go through an enumeration of the rational numbers trying to find an r such that r · 0 = n.
In this case, we can narrow the domain Z of operator A to subsets F of Z, and the codomain U of A to a certain subset of U. Studies have shown that the expansion method can successfully solve inverse problems [9, 10].
For the variation of the distribution per se, the codomain of the density function is compressed to larger numbers; therefore, in most cases, we have V a r(X k ) < V a r(X).
Replacing the real numbers, as the codomain of a metric, by an ordered Banach space we obtain a generalization of metric space.
The idea of cone metric spaces is to replace the codomain of a metric from the set of real numbers to an ordered Banach space.
A new impulse to the theory of such spaces was given by Huang and Zhang [5] when they reintroduced cone metric spaces replacing the set of real numbers by a cone in a Banach space, as the codomain of a metric (such spaces were known earlier under the name of K-metric spaces, see [6]).
The codomain of the cosine similarity function is a real number whose value is between zero and one inclusive.
