Ordered Sets and Order Homomorphisms

  • Douglas S. Bridges
  • Ghanshyam B. Mehta
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 422)


In Section 1 we describe the fundamental notions of the theory of ordered sets and of order homomorphisms [order preserving mappings) between such sets. Sections 2 and 3 deal respectively with order homomorphisms on finite and countable ordered sets. In Section 4 we discuss various order separability conditions which lead to representations of orders on uncountable sets. In Section 5, with the help of material from Section 4, we apply Cantor’s two theorems on the existence of order homomorphisms. The final section, Section 6, introduces the link between orders and topologies.


Binary Relation Weak Order Order Interval Order Topology Countable Subset 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Douglas S. Bridges
    • 1
  • Ghanshyam B. Mehta
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of WaikatoHamiltonNew Zealand
  2. 2.Department of EconomicsUniversity of QueenslandBrisbaneAustralia

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