Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample
Suppose C is a cone contained in real vector space V. When does V contain a hyperplane H that intersects each of the 0-rays in C∖{0} exactly once? We build on results found in Aliprantis, Tourky, and Klee Jr.’s work to give a partial answer to this question. We also present an example of a salient,...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2016/9623090 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832553043132940288 |
|---|---|
| author | Chris McCarthy |
| author_facet | Chris McCarthy |
| author_sort | Chris McCarthy |
| collection | DOAJ |
| description | Suppose C is a cone contained in real vector space V. When does V contain a hyperplane H that intersects each of the 0-rays in C∖{0} exactly once? We build on results found in Aliprantis, Tourky, and Klee Jr.’s work to give a partial answer to this question. We also present an example of a salient, closed Banach space cone C for which there does not exist a hyperplane that intersects each 0-ray in C∖{0} exactly once. |
| format | Article |
| id | doaj-art-29df4e3964564e48ab3f0fe366795ec6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-29df4e3964564e48ab3f0fe366795ec62025-02-03T05:57:08ZengWileyAbstract and Applied Analysis1085-33751687-04092016-01-01201610.1155/2016/96230909623090Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space CounterexampleChris McCarthy0Department of Mathematics, Borough of Manhattan Community College, City University of New York, New York City, NY 10007, USASuppose C is a cone contained in real vector space V. When does V contain a hyperplane H that intersects each of the 0-rays in C∖{0} exactly once? We build on results found in Aliprantis, Tourky, and Klee Jr.’s work to give a partial answer to this question. We also present an example of a salient, closed Banach space cone C for which there does not exist a hyperplane that intersects each 0-ray in C∖{0} exactly once.http://dx.doi.org/10.1155/2016/9623090 |
| spellingShingle | Chris McCarthy Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample Abstract and Applied Analysis |
| title | Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample |
| title_full | Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample |
| title_fullStr | Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample |
| title_full_unstemmed | Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample |
| title_short | Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample |
| title_sort | hyperplanes that intersect each ray of a cone once and a banach space counterexample |
| url | http://dx.doi.org/10.1155/2016/9623090 |
| work_keys_str_mv | AT chrismccarthy hyperplanesthatintersecteachrayofaconeonceandabanachspacecounterexample |