Elements of the topology of plane sets of points [reprinted 2-nd edition]

This book provides an elementary introduction to the ideas and methods of topology by the detailed study of certain topi

783 108 2MB

English Pages 214 [110] Year 1964

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Elements of the topology of plane sets of points [reprinted 2-nd edition]

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M. H. A. Newman

Table of contents :
Chapter 1. SETS
§ 1. The calculus of sets
§ 2. Enumerable and non-enumerable sets
Chapter II. CLOSED SETS AND OPEN SETS IN METRIC SPACES
§ 1. Closed and open sets
§ 2. Convergent sequences of points. Compact sets
§ 3. Induced structure. Relative and absolute properties
§ 4. Complete spaces
Chapter III. HOMEOMORPHISM AND CONTINUOUS MAPPINGS
§ 1. Equivalent metrics. Topological spaces. Homeomorphism
§ 2. Continuous mappings
Chapter IV. CONNECTION
§ 1. Connected sets
§ 2. Components
§ 3. Connection in compact spaces
§ 4. Local connection
§ 5. Topological characterisation of segment and circle
Chapter V. SEPARATION THEOREMS
§ 1. Chains on a grating
§ 2. Alexander’s Lemma and Jordan’s Theorem
§ 3. Invariance of dimension number and of open sets
§ 4. Further separation theorems
§ 5. Extension to sets of points in Z^p and R^p
Chapter VI. SIMPLY- AND MULTIPLY-CONNECTED PLANE
DOMAINS
§ 1. Simply-connected domains
§ 2. Mapping on a standard domain
§ 3. Connectivity of open sets
§ 4. Relations of a domain to its frontier
§ 5. Topological mapping of Jordan domains and their
closures
Chapter VII. HOMOTOPY PROPERTIES
§ 1. Paths and deformations
§ 2. Intersection and orientation of paths in R^2

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