A linear ordering is said to be representable if it can be order-embedded into the reals. Representable linear orderings have been characterized as those which are separable in the order topology and have at most countably many jumps. We use this characterization to study the representability of a lexicographic product of linear orderings. First we count the jumps in a lexicographic product in terms of the number of jumps in its factors. Then we relate the separability of a lexicographic product to properties of its factors, and derive a classification of representable lexicographic products.
Representable Lexicographic Products
GIARLOTTA, Alfio
2004-01-01
Abstract
A linear ordering is said to be representable if it can be order-embedded into the reals. Representable linear orderings have been characterized as those which are separable in the order topology and have at most countably many jumps. We use this characterization to study the representability of a lexicographic product of linear orderings. First we count the jumps in a lexicographic product in terms of the number of jumps in its factors. Then we relate the separability of a lexicographic product to properties of its factors, and derive a classification of representable lexicographic products.File in questo prodotto:
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