Ordered Sets

An Introduction
2003
ISBN: 978-0-8176-4128-3
Verlag: Birkhäuser

Buch, Englisch, 391 Seiten, Book, Format (B × H): 155 mm x 235 mm, Gewicht: 1670 g

An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.

Zielgruppe

Research

Autoren/Hrsg.

Schroeder, Bernd

Fachgebiete

• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

Preface * List of Figures * The Basics * Chains, Antichains and Fences * Upper and Lower Bounds * Retractions * Lattices * Truncated Lattices * The Dimension of Ordered Sets * Interval Orders * Lexicographic Sums * Sets P^Q = Hom (Q, P) and Products * Enumeration * Algorithmic Aspects * Appendix A: A Primer on Algebraic Topology * Appendix B: Order vs. Analysis * References * Index