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...

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Bibliographic Details
Main Author: Goff, William Sidney
Language:English
Published: University of British Columbia 2011
Subjects:
Online Access:http://hdl.handle.net/2429/34026
Description
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