
Topics on Continua
Sergio Macias(Author)
Taylor & Francis (Publisher)
1st Edition
Published on 26. May 2005
Book
Hardback
374 pages
978-0-8493-3738-3 (ISBN)
Description
Specialized as it might be, continuum theory is one of the most intriguing areas in mathematics. However, despite being popular journal fare, few books have thoroughly explored this interesting aspect of topology.
In Topics on Continua, Sergio Macias, one of the field's leading scholars, presents four of his favorite continuum topics: inverse limits, Jones's set function T, homogenous continua, and n-fold hyperspaces, and in doing so, presents the most complete set of theorems and proofs ever contained in a single topology volume. Many of the results presented have previously appeared only in research papers, and some appear here for the first time.
After building the requisite background and exploring the inverse limits of continua, the discussions focus on Professor Jones's set function T and continua for which T is continuous. An introduction to topological groups and group actions lead to a proof of Effros's Theorem, followed by a presentation of two decomposition theorems. The author then offers an in-depth study of n-fold hyperspaces. This includes their general properties, conditions that allow points of n-fold symmetric products to be arcwise accessible from their complement, points that arcwise disconnect the n-fold hyperspaces, the n-fold hyperspaces of graphs, and theorems relating n-fold hyperspaces and cones. The concluding chapter presents a series of open questions on each topic discussed in the book.
With more than a decade of teaching experience, Macias is able to put forth exceptionally cogent discussions that not only give beginning mathematicians a strong grounding in continuum theory, but also form an authoritative, single-source guide through some of topology's most captivating facets.
In Topics on Continua, Sergio Macias, one of the field's leading scholars, presents four of his favorite continuum topics: inverse limits, Jones's set function T, homogenous continua, and n-fold hyperspaces, and in doing so, presents the most complete set of theorems and proofs ever contained in a single topology volume. Many of the results presented have previously appeared only in research papers, and some appear here for the first time.
After building the requisite background and exploring the inverse limits of continua, the discussions focus on Professor Jones's set function T and continua for which T is continuous. An introduction to topological groups and group actions lead to a proof of Effros's Theorem, followed by a presentation of two decomposition theorems. The author then offers an in-depth study of n-fold hyperspaces. This includes their general properties, conditions that allow points of n-fold symmetric products to be arcwise accessible from their complement, points that arcwise disconnect the n-fold hyperspaces, the n-fold hyperspaces of graphs, and theorems relating n-fold hyperspaces and cones. The concluding chapter presents a series of open questions on each topic discussed in the book.
With more than a decade of teaching experience, Macias is able to put forth exceptionally cogent discussions that not only give beginning mathematicians a strong grounding in continuum theory, but also form an authoritative, single-source guide through some of topology's most captivating facets.
More details
Language
English
Place of publication
London
United Kingdom
Target group
Professional and scholarly
Academic and Professional Practice & Development
Product notice
sewn/stitched
Cloth over boards
Dimensions
Height: 246 mm
Width: 156 mm
Thickness: 26 mm
Weight
667 gr
ISBN-13
978-0-8493-3738-3 (9780849337383)
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Schweitzer Classification
Other editions
Additional editions

Sergio Macias
Topics on Continua
Book
12/2019
1st Edition
Chapman & Hall/CRC
€76.81
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Sergio Macias
Topics on Continua
E-Book
05/2005
1st Edition
Chapman & Hall/CRC
€86.99
Available for download

Sergio Macias
Topics on Continua
E-Book
05/2005
1st Edition
Chapman & Hall/CRC
€86.99
Available for download
Person
Macias, Sergio
Content
Preliminaries, including an introduction to Product Topology. Inverse Limits and Related Topics. Jones Set Function T. A Theorem of E.G. Effros. Decomposition Theorems. n-Fold Hyperspaces. Questions.