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Some problems on mountain climbing Hung, Patrick Chia-Ling
Abstract
Let f and g be two continuous, real-valued functions defined on [0,1] with f(0) = g(0) and f(l) = g(l). The main result of this thesis is to characterize the property that (0,0) and (1,1) are in the same connected component of G(f,g) = {(x,y)|f(x)=g(y)}. In Chapter I, we study conditions implying that (0,0) and (1,1) are in the same connected component of G(f,g), where f and. g are not necessarily real-valued functions. We obtain theorems to characterize [0,1], In Chapter II, we give a simple proof of a theorem by Sikorski and Zarankiewicz. In Chapter III, we obtain our main result. In Chapter IV, we study pathwise connectedness in G(f,g) and give some applications. In Chapter V, we study the question of sliding a chord of given length along a path. An example is given to show that this is not always possible.
Item Metadata
Title |
Some problems on mountain climbing
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1973
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Description |
Let f and g be two continuous, real-valued functions defined on [0,1] with f(0) = g(0) and f(l) = g(l). The main result of this thesis is to characterize the property that (0,0) and (1,1) are in the same connected component of G(f,g) = {(x,y)|f(x)=g(y)}.
In Chapter I, we study conditions implying that (0,0) and (1,1) are in the same connected component of G(f,g), where f and. g are not necessarily real-valued functions. We obtain theorems to characterize [0,1],
In Chapter II, we give a simple proof of a theorem by Sikorski and Zarankiewicz.
In Chapter III, we obtain our main result.
In Chapter IV, we study pathwise connectedness in G(f,g) and give some applications.
In Chapter V, we study the question of sliding a chord of given length along a path. An example is given to show that this is not always possible.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-03-04
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Provider |
Vancouver : University of British Columbia Library
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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.
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DOI |
10.14288/1.0080475
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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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.