| Description |
1 online resource (82 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society ; number 125 |
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Memoirs of the American Mathematical Society ; no. 125.
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| Contents |
TABLE OF CONTENTS -- 1. INTRODUCTION AND BASIC DEFINITIONS -- Definition of half-ray curve and real curve -- Structure Theorem for Half-ray Curves -- Embedding Theorem for Half-ray Curves -- Definition of K[sub(+)], K_, and singular sets -- Remark 1.1 -- 2. STRUCTURE THEOREMS -- Structure Theorem for K[sub(+)] and K_ -- Structure Theorem for Real Curves -- Corollary 2.1 -- 3. PARAMETERIZATION -- Parameterization Theorem -- 4. SOME EXAMPLES OF REAL CURVES -- Figure 1 -- ""Moby Dick"" -- Figure 2 (i) and Figure 2 (ii) -- Figure 3 -- ""Coffee-percolator"" -- Figure 4 -- ""Upside-down-elephant"" |
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Figure 5 -- ""Badly-cracked-egg"" -- Figure 6 -- ""Fry-pan-on-a-grill"" -- Figure 7 -- ""Spider-on-a-thread"" -- 5. EMBEDDING -- Embedding Theorem for Real Curves -- Definition of noose-like chain -- Definition of property y -- Definition of (e, n)-admissible link with center x[sub(1)] -- Definition of ""admissible"" noose-like chain -- Definition of admissible component of S, A(S) -- Remark 5.1 -- Definition of standard embedding of in the plane -- Lemma 5.6 -- Non-embeddability Theorem -- 6. MORE ABOUT EMBEDDINGS OF REAL CURVES -- Definition of standard embedding of M in the plane |
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Planar Embedding Theorem for Real Curves -- Definition of admissible pattern with respect to N[sub(1)] beyond u -- Toroidal Embedding Theorem -- Two-manifold Embedding Theorem -- Problem 6.1 -- Theorem on Weak Chainability of Planar Real Curves -- Problem 6.2 -- 7. THE MORE GENERAL CONDITION OF LOCAL COMPACTNESS -- Theorem 7.2 -- REFERENCES |
| Bibliography |
Includes bibliographical references (page 74) |
| Notes |
English |
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Print version record |
| Subject |
Metric spaces.
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Continuity.
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Manifolds (Mathematics)
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Curves.
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Topological imbeddings.
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Continuity
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Curves
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Manifolds (Mathematics)
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Metric spaces
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Topological imbeddings
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| Form |
Electronic book
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| Author |
Quinn, Joseph, author
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| ISBN |
9780821899236 |
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0821899236 |
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