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Set Function T

An Account on F. B. Jones' Contributions to Topology

  • Book
  • © 2021

Overview

Authors:
  1. Sergio Macías

    1. Instituto de Matemáticas, National Autonomous University of Mexico, Ciudad de México, Mexico

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  • Presents the set function \mathcal{T}, of great importance to the study of continuum theory, in a clear and structured way
  • Starts with a gentle introductory chapter, gradually advancing towards modern applications
  • Brings open problems that can potentially encourage topologists to advance in the field

Part of the book series: Developments in Mathematics (DEVM, volume 67)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Preliminaries

    • Sergio Macías
    Pages 1-48

  3. The Set Function \({\mathcal {T}}\)

    • Sergio Macías
    Pages 49-93

  4. Decomposition Theorems

    • Sergio Macías
    Pages 95-122

  5. \(\mathcal {T}\)-Closed Sets

    • Sergio Macías
    Pages 123-143

  6. Continuity of \(\mathcal {T}\)

    • Sergio Macías
    Pages 145-166

  7. Images of \(\mathcal {T}\)

    • Sergio Macías
    Pages 167-182

  8. Applications

    • Sergio Macías
    Pages 183-211

  9. Questions

    • Sergio Macías
    Pages 213-216

  10. Back Matter

    Pages 217-225
    Download chapter PDF
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Keywords

About this book

This book presents, in a clear and structured way, the set function \mathcal{T} and how it evolved since its inception by Professor F. Burton Jones in the 1940s. It starts with a very solid introductory chapter, with all the prerequisite material for navigating through the rest of the book. It then gradually advances towards the main properties, Decomposition theorems, \mathcal{T}-closed sets, continuity and images, to modern applications.
The set function \mathcal{T} has been used by many mathematicians as a tool to prove results about the semigroup structure of the continua, and about the existence of a metric continuum that cannot be mapped onto its cone or to characterize spheres. Nowadays, it has been used by topologists worldwide to investigate open problems in continuum theory.


This book can be of interest to both advanced undergraduate and graduate students, and to experienced researchers as well. Its well-defined structure make this book suitable not only for self-study but also as support material to seminars on the subject. Its many open problems can potentially encourage mathematicians to contribute with further advancements in the field.



Authors and Affiliations

  • Instituto de Matemáticas, National Autonomous University of Mexico, Ciudad de México, Mexico

    Sergio Macías

About the author

Sergio Macías is a Professor at the Institute of Mathematics of the National Autonomous University of Mexico (UNAM). He got a Master’s degree from the same university, and a PhD from Tulane University, New Orleans, USA. His research interests lie on topology with works on continuum theory and hyperspaces of continua. Dr. Macías also authored the book “Topics on Continua” (2018, ISBN 978-3-319-90901-1), whose second edition was published by Springer.

Bibliographic Information

  • Book Title: Set Function T

  • Book Subtitle: An Account on F. B. Jones' Contributions to Topology

  • Authors: Sergio Macías

  • Series Title: Developments in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-65081-0

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-65080-3Published: 20 March 2021

  • Softcover ISBN: 978-3-030-65083-4Published: 20 March 2022

  • eBook ISBN: 978-3-030-65081-0Published: 19 March 2021

  • Series ISSN: 1389-2177

  • Series E-ISSN: 2197-795X

  • Edition Number: 1

  • Number of Pages: XIV, 225

  • Number of Illustrations: 32 b/w illustrations

  • Topics: Topology, Geometry

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