A simple closed curve which fails to pierce a disc at only one point
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 s...
| Main Author: | |
|---|---|
| Language: | English |
| Published: |
University of British Columbia
2011
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/2429/34026 |
| id |
ndltd-UBC-oai-circle.library.ubc.ca-2429-34026 |
|---|---|
| record_format |
oai_dc |
| spelling |
ndltd-UBC-oai-circle.library.ubc.ca-2429-340262018-01-05T17:47:17Z A simple closed curve which fails to pierce a disc at only one point Goff, William Sidney Curves 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. Science, Faculty of Mathematics, Department of Graduate 2011-04-27T16:47:38Z 2011-04-27T16:47:38Z 1972 Text Thesis/Dissertation http://hdl.handle.net/2429/34026 eng 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. University of British Columbia |
| collection |
NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Curves |
| spellingShingle |
Curves Goff, William Sidney A simple closed curve which fails to pierce a disc at only one point |
| 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. === Science, Faculty of === Mathematics, Department of === Graduate |
| author |
Goff, William Sidney |
| author_facet |
Goff, William Sidney |
| author_sort |
Goff, William Sidney |
| title |
A simple closed curve which fails to pierce a disc at only one point |
| title_short |
A simple closed curve which fails to pierce a disc at only one point |
| title_full |
A simple closed curve which fails to pierce a disc at only one point |
| title_fullStr |
A simple closed curve which fails to pierce a disc at only one point |
| title_full_unstemmed |
A simple closed curve which fails to pierce a disc at only one point |
| title_sort |
simple closed curve which fails to pierce a disc at only one point |
| publisher |
University of British Columbia |
| publishDate |
2011 |
| url |
http://hdl.handle.net/2429/34026 |
| work_keys_str_mv |
AT goffwilliamsidney asimpleclosedcurvewhichfailstopierceadiscatonlyonepoint AT goffwilliamsidney simpleclosedcurvewhichfailstopierceadiscatonlyonepoint |
| _version_ |
1718595108360683520 |