Frames and Locales

Topology without points

  • Jorge Picado
  • Aleš Pultr

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Jorge Picado, Aleš Pultr
    Pages 1-8
  3. Jorge Picado, Aleš Pultr
    Pages 9-22
  4. Jorge Picado, Aleš Pultr
    Pages 23-48
  5. Jorge Picado, Aleš Pultr
    Pages 49-72
  6. Jorge Picado, Aleš Pultr
    Pages 73-97
  7. Jorge Picado, Aleš Pultr
    Pages 99-123
  8. Jorge Picado, Aleš Pultr
    Pages 125-144
  9. Jorge Picado, Aleš Pultr
    Pages 145-167
  10. Jorge Picado, Aleš Pultr
    Pages 169-181
  11. Jorge Picado, Aleš Pultr
    Pages 183-202
  12. Jorge Picado, Aleš Pultr
    Pages 203-226
  13. Jorge Picado, Aleš Pultr
    Pages 227-252
  14. Jorge Picado, Aleš Pultr
    Pages 253-267
  15. Jorge Picado, Aleš Pultr
    Pages 269-296
  16. Jorge Picado, Aleš Pultr
    Pages 297-314
  17. Back Matter
    Pages 315-398

About this book

Introduction

Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the 1920s offered an expression of the geometric intuition of a "realistic" place (spot, grain) of non-trivial extent.

Imitating the behaviour of open sets and their relations led to a new approach to topology flourishing since the end of the 1950s. It has proved to be beneficial in many respects. Neglecting points, only little information was lost, while deeper insights have been gained; moreover, many results previously dependent on choice principles became constructive. The result is often a smoother, rather than a more entangled, theory.

No monograph of this nature has appeared since Johnstone's celebrated Stone Spaces in 1983. The present book is intended as a bridge from that time to the present. Most of the material appears here in book form for the first time or is presented from new points of view. Two appendices provide an introduction to some requisite concepts from order and category theories.

Keywords

Categorical topology Lattice theory Order theory

Authors and affiliations

  • Jorge Picado
    • 1
  • Aleš Pultr
    • 2
  1. 1., CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal
  2. 2., Department of Applied Mathematics (KAM)MFF Karlovy UniversityPrague 1Czech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0154-6
  • Copyright Information Springer Basel AG 2012
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0153-9
  • Online ISBN 978-3-0348-0154-6
  • Series Print ISSN 1660-8046
  • Series Online ISSN 1660-8054
  • About this book