Embeddability and Structure Properties of Real Curves.

Intro -- 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 -- 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 (δ, λ)-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 -- 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.