Dualities and endomorphisms of pseudo-cones

TL;DR

This paper investigates the structure of closed pseudo-cones, introduces a unique duality for them, and classifies their endomorphisms, enhancing understanding of their mathematical properties.

Contribution

It presents a new duality for closed pseudo-cones and characterizes this duality as essentially unique, along with classifying their endomorphisms.

Findings

The duality characterizes closed pseudo-cones uniquely.

The duality is essentially the only possible abstract duality for these sets.

Endomorphisms of closed pseudo-cones are classified based on this duality.

Abstract

In this paper we study a class of convex sets which are called closed pseudo-cones and study a new duality of this class. It turns out that the duality characterizes closed pseudo-cones and is essentially the only possible abstract duality of them.The characterization of the duality is corresponding to the classification of endomorphisms closed pseudo-cones.