The Continuity of $\mathbb{Q}_+$-Homogeneous Superadditive Correspondences

TL;DR

This paper studies the conditions under which certain superadditive correspondences, which are homogeneous with respect to positive rationals, are continuous, and shows they have continuous linear selections under specific conditions.

Contribution

It establishes the continuity criteria for $Q_+$-homogeneous superadditive correspondences and demonstrates the existence of continuous linear selections for lower semicontinuous cases.

Findings

Continuity of $Q_+$-homogeneous superadditive correspondences is characterized.

Every lower semicontinuous $Q_+$-homogeneous superadditive correspondence admits continuous linear selections.

Results apply to correspondences defined on cones with finite basis in real topological vector spaces.

Abstract

In this paper we investigate the continuity of $\mathbb{Q}_+$-homogeneous superadditive correspondences defined on the cones with finite basis in real topological vector spaces. It is also shown that every lower semicontinuous and $\mathbb{Q}_+$-homogeneous superadditive correspondence between two cones with finite basis admits a family of continuous linear selections.