Detailed Information
Cited 0 time in 
Cited 0 time in 
Cited 0 time in
Metadata Downloads
On a Construction of Plane Sets with Pre-assigned Metric DimensionsOn a Construction of Plane Sets with Pre-assigned Metric Dimensions
- Other Titles
- On a Construction of Plane Sets with Pre-assigned Metric Dimensions
- Authors
- SOON-MO JUNG; BO-HYUN CHUNG; BYUNGBAE KIM
- Issue Date
- Jun-2002
- Publisher
- 경북대학교 자연과학대학 수학과
- Keywords
- metric dimension; Hausdorff dimension; mesh
- Citation
- Kyungpook Mathematical Journal, v.42, no.1, pp.95 - 102
- Journal Title
- Kyungpook Mathematical Journal
- Volume
- 42
- Number
- 1
- Start Page
- 95
- End Page
- 102
- ISSN
- 1225-6951
- Abstract
- In this paper, some results of S.-M. Jung[3] will be generalized as follows: For a given 0<r<2, a compact and uncountable plane set Cr which satisfies dim_B C_r=r and ,for all ,shall be constructed. This gives negative answers to the question whether Marstrand's theorem is also true when 'Hausdorff dimension's in the statement of the theorem are replaced by 'metric dimension's. In the case when 0<s<1, we shall investigate a method to construct compact uncountable plane sets E with .Furthermore, we shall construct a compact and uncountable plane set F with dim_B F>1 and dim_B proj F=1 for all .
- Files in This Item
- There are no files associated with this item.
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
Related Researcher
- Kim, Byung bae
- Science & Technology (Science & Technology)