A family of pseudo metrics on B^3 and its application
| dc.creator | Kim, Young Deuk | |
| dc.date | 2002-01-10 | |
| dc.date | 2007-02-15 | |
| dc.date.accessioned | 2026-07-07T07:46:50Z | |
| dc.date.available | 2026-07-07T07:46:50Z | |
| dc.description | Let B^3 be the closed unit ball in R^3 and S^2 its boundary. We define a family of pseudo metrics on B^3. As an application, We prove that for any countable-to-one function f:S^2\to [0,a], the set NM^n_f={x\in S^2 | there exists y\in S^2 such that f(x)-f(y)>nd_E(x,y)} is uncountable for all natural number n, where d_E is the Euclidean metric on R^3. | |
| dc.description | 14 pages, 5 figures, A section of v3 is appeared on Rocky Mountain Journal of Mathematics 36(2006) no.6 1927-1935. Similar construction is in GN/0702453 | |
| dc.identifier | https://arxiv.org/abs/math/0201077 | |
| dc.identifier | http://arxiv.org/abs/math/0201077 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123958 | |
| dc.subject | General Topology | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N05(primary), 57M40(secondary) | |
| dc.title | A family of pseudo metrics on B^3 and its application | |
| dc.type | text |