On Lipschitz ball noncollapsing functions and uniform co-Lipschitz mappings of the plane
We give a sharp estimate on the cardinality of point preimages of a uniform co-Lipschitz mapping on the plane. We also give a necessary and sufficient condition for a ball noncollapsing Lipschitz function to have a point with infinite preimage.
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA.2005.543 |
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| _version_ | 1832562441456713728 |
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| author | Olga Maleva |
| author_facet | Olga Maleva |
| author_sort | Olga Maleva |
| collection | DOAJ |
| description | We give a sharp estimate on the cardinality of point preimages of a uniform co-Lipschitz mapping on the plane. We also give a necessary and sufficient condition for a ball noncollapsing Lipschitz function to have a point with infinite preimage. |
| format | Article |
| id | doaj-art-0969f46bd7de4ca89fbbdde60dde98cf |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0969f46bd7de4ca89fbbdde60dde98cf2025-02-03T01:22:36ZengWileyAbstract and Applied Analysis1085-33751687-04092005-01-012005554356210.1155/AAA.2005.543On Lipschitz ball noncollapsing functions and uniform co-Lipschitz mappings of the planeOlga Maleva0Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, IsraelWe give a sharp estimate on the cardinality of point preimages of a uniform co-Lipschitz mapping on the plane. We also give a necessary and sufficient condition for a ball noncollapsing Lipschitz function to have a point with infinite preimage.http://dx.doi.org/10.1155/AAA.2005.543 |
| spellingShingle | Olga Maleva On Lipschitz ball noncollapsing functions and uniform co-Lipschitz mappings of the plane Abstract and Applied Analysis |
| title | On Lipschitz ball noncollapsing functions and uniform co-Lipschitz mappings of the plane |
| title_full | On Lipschitz ball noncollapsing functions and uniform co-Lipschitz mappings of the plane |
| title_fullStr | On Lipschitz ball noncollapsing functions and uniform co-Lipschitz mappings of the plane |
| title_full_unstemmed | On Lipschitz ball noncollapsing functions and uniform co-Lipschitz mappings of the plane |
| title_short | On Lipschitz ball noncollapsing functions and uniform co-Lipschitz mappings of the plane |
| title_sort | on lipschitz ball noncollapsing functions and uniform co lipschitz mappings of the plane |
| url | http://dx.doi.org/10.1155/AAA.2005.543 |
| work_keys_str_mv | AT olgamaleva onlipschitzballnoncollapsingfunctionsanduniformcolipschitzmappingsoftheplane |