- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- A simple closed curve which fails to pierce a disc...
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
A simple closed curve which fails to pierce a disc at only one point Goff, William Sidney
Abstract
A simple closed curve J is constructed in R³ which fails to pierce a disc at only one point. The intersections of various surfaces in R³ are investigated to prove that J has the desired property. Heavy use is made of approximation of surfaces in R³ with polyhedral surfaces. J is used to construct simple closed curves which fail to pierce discs at various finite and infinite sets of points. The most interesting of these is a simple closed curve which pierces a disc at one dense set of points while failing to pierce a disc at another dense set of points which has measure 0.
Item Metadata
| Title |
A simple closed curve which fails to pierce a disc at only one point
|
| Creator | |
| Publisher |
University of British Columbia
|
| Date Issued |
1972
|
| Description |
A simple closed curve J is constructed in R³ which fails to pierce a disc at only one point. The intersections of various surfaces in R³ are investigated to prove that J has the desired property. Heavy use is made of approximation of surfaces in R³ with polyhedral surfaces.
J is used to construct simple closed curves which fail to pierce discs at various finite and infinite sets of points. The most interesting of these is a simple closed curve which pierces a disc at one dense set of points while failing to pierce a disc at another dense set of points which has measure 0.
|
| Genre | |
| Type | |
| Language |
eng
|
| Date Available |
2011-04-27
|
| Provider |
Vancouver : University of British Columbia Library
|
| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
|
| DOI |
10.14288/1.0080456
|
| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
|
| Campus | |
| Scholarly Level |
Graduate
|
| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.