TY - THES
AU - Hung, Patrick Chia-Ling
PY - 1973
TI - Some problems on mountain climbing
KW - Thesis/Dissertation
LA - eng
M3 - Text
AB - 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.
N2 - 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.
UR - https://open.library.ubc.ca/collections/831/items/1.0080475
ER - End of Reference