Continuum Theory (Paperback)

Alejandro Illanes

ISBN 10: 3031910109 / ISBN 13: 9783031910104

Published by Springer International Publishing AG, Cham, 2025

About this Item

Paperback. This graduate textbook provides a natural and structured introduction to Continuum Theory, guiding readers from fundamental concepts to advanced topics. It covers classical results such as locally connected continua, indecomposable continua, arcs, circles, finite graphs, dendroids, and the relationship between the Cantor set and continua. The second half explores the theory of hyperspaces, presenting various models, their properties, and key theorems, while also highlighting elegant and lesser-known mathematical results.Designed for readers with an understanding of basic topology, this book serves as a valuable resource for PhD students and researchers in mathematics. It offers a rigorous and thorough approach, with detailed proofs that clarify complex argumentsespecially regarding the intricate properties of the pseudo-arc. A wealth of exercises helps reinforce understanding and develop problem-solving skills.This book stands out for its depth and breadth, covering a range of topics. It provides a comprehensive study of hyperspace models, the homogeneity of the Hilbert cube, and the pseudo-arc, offering one of the few accessible and complete proofs of its unique properties. With its structured progression and careful exposition, this book is a valuable reference for anyone interested in continuum theory. The second half explores the theory of hyperspaces, presenting various models, their properties, and key theorems, while also highlighting elegant and lesser-known mathematical results.Designed for readers with an understanding of basic topology, this book serves as a valuable resource for PhD students and researchers in mathematics. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9783031910104

Bibliographic Details

• Title: Continuum Theory (Paperback)
• Publisher: Springer International Publishing AG, Cham
• Publication Date: 2025
• Language: English
• ISBN 10: 3031910109
• ISBN 13: 9783031910104
• Binding: Paperback
• Condition: new

About this title

Synopsis

This graduate textbook provides a natural and structured introduction to Continuum Theory, guiding readers from fundamental concepts to advanced topics. It covers classical results such as locally connected continua, indecomposable continua, arcs, circles, finite graphs, dendroids, and the relationship between the Cantor set and continua. The second half explores the theory of hyperspaces, presenting various models, their properties, and key theorems, while also highlighting elegant and lesser-known mathematical results.

Designed for readers with an understanding of basic topology, this book serves as a valuable resource for PhD students and researchers in mathematics. It offers a rigorous and thorough approach, with detailed proofs that clarify complex arguments—especially regarding the intricate properties of the pseudo-arc. A wealth of exercises helps reinforce understanding and develop problem-solving skills.

This book stands out for its depth and breadth, covering a range of topics. It provides a comprehensive study of hyperspace models, the homogeneity of the Hilbert cube, and the pseudo-arc, offering one of the few accessible and complete proofs of its unique properties. With its structured progression and careful exposition, this book is a valuable reference for anyone interested in continuum theory.

About the Author

Alejandro Illanes is a researcher at the National Autonomous University of Mexico, where he has taught for over 45 years. He has over 150 research papers in international journals and has supervised 16 doctoral theses. He is the author of a number of books.