Embeddability and structure properties of real curves / by Sam B. Nadler, Jr. and J. Quinn.

Format:

Book

Author/Creator:

Nadler, Sam B., author.

Contributor:

Quinn, Joseph, joint author.

Series:

Memoirs of the American Mathematical Society ; no. 125.

Memoirs of the American Mathematical Society ; number 125

Language:

English

Subjects (All):

Metric spaces.

Continuity.

Manifolds (Mathematics).

Curves.

Topological imbeddings.

Physical Description:

1 online resource (82 p.)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, [1972]

Language Note:

English

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""""""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 (Î?, 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 â?? 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""

Notes:

Description based upon print version of record.

Bibliography: pages 74.

Description based on print version record.

ISBN:

0-8218-9923-6