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Shuffling of Linear Orders

Published online by Cambridge University Press:  20 November 2018

John Lindsay Orr
John Lindsay Orr*
Affiliation:
Department of Mathematics and Statistics, University of Nebraska—Lincoln, Lincoln, Nebraska 68588-0323, U.S.A. e-mail: jorr@math.unl.edu
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Abstract

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A linearly ordered set A is said to shuffle into another linearly ordered set B if there is an order preserving surjection A —> B such that the preimage of each member of a cofinite subset of B has an arbitrary pre-defined finite cardinality. We show that every countable linearly ordered set shuffles into itself. This leads to consequences on transformations of subsets of the real numbers by order preserving maps.

Keywords

06A05

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 2 , 01 June 1995 , pp. 223 - 229
Copyright
Copyright © Canadian Mathematical Society 1995

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