Elements of Combinatorial and Differential Topology

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American Mathematical Soc. - Mathematics - 331 pages
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Contents

IV
5
V
29
VI
47
VII
55
VIII
63
IX
72
X
87
XI
99
XVII
161
XVIII
181
XIX
199
XX
207
XXI
220
XXII
239
XXIII
257
XXIV
266

XII
117
XIII
130
XIV
139
XV
149
XVI
157
XXV
279
XXVI
291
XXVII
317
XXVIII
325
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Page 8 - Kuratowski [5] proved the classic theorem that a graph is nonplanar if and only if it contains a subgraph homeomorphic to K$ or K*,i.
Page 13 - A given planar graph is outerplanar iff it can be embedded in the plane in such a way that all nodes lie on an external infinite face.
Page 1 - A, and the interior of A is the union of all open sets contained in A. The most important example of a topological space is the Euclidean space Rn. The open sets in R" are the balls D% = {xe R" : ||z - a|| < e} and all their unions.
Page 2 - If X is a topological space and Y is a subset of X, then Y can be endowed with the induced topology, which consists of the intersections of Y with open subsets of X. This turns the sphere 5" = {x € K"+1 : \\x\\ = 1} into a topological space.

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