Volume 34, Issue 2
Theorems of Helly's Type for Partially-Closed Half-Spaces

Jian-Guo Liu & Qi Guo

Commun. Math. Res., 34 (2018), pp. 117-124.

Published online: 2019-12

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  • 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.

  • Keywords

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

  • AMS Subject Headings

52A20, 52A38, 52A39, 52A40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

249061306@qq.com (Jian-Guo Liu)

guoqi@mail.usts.edu.cn (Qi Guo)

  • BibTex
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  • TXT
@Article{CMR-34-117, author = {Liu , Jian-Guo and Guo , Qi}, title = {Theorems of Helly's Type for Partially-Closed Half-Spaces}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {2}, pages = {117--124}, 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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.02.03}, url = {http://global-sci.org/intro/article_detail/cmr/13516.html} }
TY - JOUR T1 - Theorems of Helly's Type for Partially-Closed Half-Spaces AU - Liu , Jian-Guo AU - Guo , Qi JO - Communications in Mathematical Research VL - 2 SP - 117 EP - 124 PY - 2019 DA - 2019/12 SN - 34 DO - http://doi.org/10.13447/j.1674-5647.2018.02.03 UR - https://global-sci.org/intro/article_detail/cmr/13516.html KW - Helly's theorem, partially-closed half-space, affine function, convex set AB -

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.

Jian-Guo Liu & Qi Guo. (2019). Theorems of Helly's Type for Partially-Closed Half-Spaces. Communications in Mathematical Research . 34 (2). 117-124. doi:10.13447/j.1674-5647.2018.02.03
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