Universal entire functions that define order isomorphisms of countable real sets

2018/07/08 by Gauthier, Paul M.
#30E10 #30K20 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.02770

Abstract

In 1895, Cantor showed that between every two countable dense real sets, there is an order isomorphism. In fact, there is always such an order isomorphism, which is the restriction of a universal entire function.

Related

• On the order and the type of an entire function
• Cantor-Schröder-Bernstein theorem for a class of countable linear orders
• Interval chains and completeness in ultrapowers of ordered sets
• Banach spaces and groups - order properties and universal models
• Order-Preserving Variants of The Basic Principles of Functional Analysis