Geometric and topological properties of the Minkowski operator on convex sets

Authors

DOI:

https://doi.org/10.29229/uzmj.2026-2-24

Keywords:

Convex sets, Minkowski difference, Minkowski sum, homothetic set, boundary of a set, compact set

Abstract

This paper systematically establishes the fundamental geometrical and topological properties of the Minkowski operator on convex sets in an Euclidean space. The convexity, closedness, and boundary properties of the Minkowski sum and difference are analyzed. In addition, results concerning the Minkowski sum and difference of open and closed sets are presented. The paper also constructs illustrative examples to clarify each of the obtained results.

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Published

2026-06-12

Issue

Vol. 70 No. 2 (2026): Uzbek Mathematical Journal

Section

Published

How to Cite

Geometric and topological properties of the Minkowski operator on convex sets. (2026). Uzbek Mathematical Journal, 70(2), 208-217. https://doi.org/10.29229/uzmj.2026-2-24