Abstract
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.
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© 1995 Springer-Verlag Berlin Heidelberg
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Bridges, D.S., Mehta, G.B. (1995). Ordered Sets and Order Homomorphisms. In: Representations of Preferences Orderings. Lecture Notes in Economics and Mathematical Systems, vol 422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51495-1_1
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DOI: https://doi.org/10.1007/978-3-642-51495-1_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58839-9
Online ISBN: 978-3-642-51495-1
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