Unit-circle-preserving mappings
We prove that if a one-to-one mapping f:ℝn→ℝn(n≥2) preserves the unit circles, then f is a linear isometry up to translation.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204404098 |
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| _version_ | 1832566592682065920 |
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| author | Soon-Mo Jung Byungbae Kim |
| author_facet | Soon-Mo Jung Byungbae Kim |
| author_sort | Soon-Mo Jung |
| collection | DOAJ |
| description | We prove that if a one-to-one mapping f:ℝn→ℝn(n≥2) preserves the unit circles, then f is a linear isometry up to translation. |
| format | Article |
| id | doaj-art-0de97258f3394b04a3929e3526610ceb |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0de97258f3394b04a3929e3526610ceb2025-02-03T01:03:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004663577358610.1155/S0161171204404098Unit-circle-preserving mappingsSoon-Mo Jung0Byungbae Kim1Mathematics Section, College of Science and Technology, Hong-Ik University, Chochiwon 339-701, KoreaMathematics Section, College of Science and Technology, Hong-Ik University, Chochiwon 339-701, KoreaWe prove that if a one-to-one mapping f:ℝn→ℝn(n≥2) preserves the unit circles, then f is a linear isometry up to translation.http://dx.doi.org/10.1155/S0161171204404098 |
| spellingShingle | Soon-Mo Jung Byungbae Kim Unit-circle-preserving mappings International Journal of Mathematics and Mathematical Sciences |
| title | Unit-circle-preserving mappings |
| title_full | Unit-circle-preserving mappings |
| title_fullStr | Unit-circle-preserving mappings |
| title_full_unstemmed | Unit-circle-preserving mappings |
| title_short | Unit-circle-preserving mappings |
| title_sort | unit circle preserving mappings |
| url | http://dx.doi.org/10.1155/S0161171204404098 |
| work_keys_str_mv | AT soonmojung unitcirclepreservingmappings AT byungbaekim unitcirclepreservingmappings |