Theorems of Helly's Type for Partially-Closed Half-Spaces
Commun. Math. Res., 34 (2018), pp. 117-124.
Published online: 2019-12
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@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.
Liu , Jian-Guo and Guo , Qi. (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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