Extremal elements in hypercomplex space

TL;DR

This paper investigates extremal elements and the h-hull in n-dimensional hypercomplex space, introducing a new class of H-quasiconvex sets that extend strongly hypercomplex convex sets and are closed under intersections.

Contribution

It introduces the class of H-quasiconvex sets, expanding the understanding of convexity in hypercomplex spaces and their extremal properties.

Findings

Defined extremal elements and h-hull in hypercomplex space

Introduced H-quasiconvex sets including strongly hypercomplex convex sets

Proved closure of H-quasiconvex sets under intersections

Abstract

Extremal elements and a h-hull of sets in the n-dimensional hypercomplex space are investigated. Introduced a class of H-quasiconvex sets including strongly hypercomplex convex sets and being closed with respect to intersections.