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Ordered Sets: An Introduction with Connections from Combinatorics to Topology

✍ Scribed by Schröder, Bernd Siegfried Walter

Publisher
Birkhäuser
Year
2016
Tongue
English
Leaves
426
Edition
2ed.
Category
Library
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✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Basics....Pages 1-21
Chains, Antichains, and Fences....Pages 23-51
Upper and Lower Bounds....Pages 53-76
Retractions....Pages 77-111
Constraint Satisfaction Problems....Pages 113-153
Graphs and Homomorphisms....Pages 155-171
Lexicographic Sums....Pages 173-197
Lattices....Pages 199-226
Truncated Lattices....Pages 227-253
Dimension....Pages 255-277
Interval Orders....Pages 279-295
Sets P Q  = Hom(Q, P) and Products ....Pages 297-332
Enumeration of Ordered Sets....Pages 333-356
Back Matter....Pages 357-420

✦ Subjects

Ensembles ordonnés;Structures algébriques ordonnées;Topologie algébrique;Ordered sets;Ordered algebraic structures;Algebraic topology

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