Theorems of Helly's Type for Partially-Closed Half-Spaces

Authors

  • Jian-Guo Liu Department of Mathematics, Suzhou University of Science and Technology, Suzhou, Jiangsu, 215009
  • Qi Guo Department of Mathematics, Suzhou University of Science and Technology, Suzhou, Jiangsu, 215009

DOI:

https://doi.org/10.13447/j.1674-5647.2018.02.03

Keywords:

Helly's theorem, partially-closed half-space, affine function, convex set

Abstract

In this article, under quite weaker conditions, theorems of Helly's type for (not necessarily finite) family of partially closed half-spaces are presented in both analytic and geometric forms. Examples are also provided to show that these conditions cannot be omitted in general.

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Published

2019-12-16

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Issue

Vol. 34 No. 2 (2018)

Section

Articles

How to Cite

Theorems of Helly’s Type for Partially-Closed Half-Spaces. (2019). Communications in Mathematical Research, 34(2), 117-124. https://doi.org/10.13447/j.1674-5647.2018.02.03