Generalizing the Fixed Point Index.
Maps defined on the interior of the standard non-negative cone in which are both homogeneous of degree and order-preserving arise naturally in the study of certain classes of Discrete Event Systems. Such maps are non-expanding in Thompson’s part metric and continuous on the interior of the cone. It follows from more general results presented here that all such maps have a homogeneous order-preserving continuous extension to the whole cone. It follows that the extension must have at least...
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