Ordered Sets pp 297-332 | Cite as

Sets PQ = Hom(Q, P) and Products

  • Bernd Schröder


The order-preserving maps from one ordered set to another form a natural ordered set when given the pointwise order. Products are defined similar to these homomorphism sets. Hence we will investigate homomorphism sets and products of ordered sets in the same chapter. We will introduce some of the salient results on these sets, such as the fixed point theorem for products of two finite ordered sets (see Theorem 12.17), Hashimoto’s Refinement Theorem (see Theorem 12.30), and the cancelation property for exponents (see Theorem 12.47). The automorphism conjecture (see Open Question 2.14) as well as the open problems at the end of this chapter show that there are interesting problems related to homomorphism sets and products that remain open.


Boolean Algebra Point Property Finite Product Infinite Product Fixed Point Property 
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© Springer International Publishing 2016

Authors and Affiliations

  • Bernd Schröder
    • 1
  1. 1.Department of MathematicsUniversity of Southern MississippiHattiesburgUSA

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