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 |
Summary: | 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 |
---|