Sets P Q = Hom(Q, P) and Products

Bernd S. W. Schröder
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Bernd S. W. Schröder: Lousiana Tech University, Program of Mathematics and Statistics

Chapter 10 in Ordered Sets, 2003, pp 227-262 from Springer

Abstract: Abstract Order-preserving mappings from one ordered set to another form a natural ordered set under the pointwise order. Since products in general are defined similar to homomorphism sets, we shall investigate homomorphism sets and products of ordered sets closely together. In this chapter we introduce some of the salient results on these sets such as the fixed point theorem for products of two finite ordered sets (cf. Theorem 10.2.11), Hashimoto’s refinement theorem (cf. Theorem 10.4.4) and the cancelation property for exponents (cf. Theorem 10.5.9). The automorphism conjecture (cf. Open Question 11.5.1) 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.

Keywords: Complete Lattice; Point Property; Finite Product; Infinite Product; Fixed Point Property (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-1-4612-0053-6_10

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