Corpus ID: 119578330

# Geometric random graphs and Rado sets of continuous functions

@article{Bonato2018GeometricRG,
title={Geometric random graphs and Rado sets of continuous functions},
author={Anthony Bonato and Jeannette C. M. Janssen and Anthony Quas},
journal={arXiv: Combinatorics},
year={2018}
}
• Published 28 February 2018
• Mathematics
• arXiv: Combinatorics
We prove the existence of Rado sets in the Banach space of continuous functions on [0,1]. A countable dense set S is Rado if with probability 1, the infinite geometric random graph on S, formed by probabilistically making adjacent elements of S that are within unit distance of each other, is unique up to isomorphism. We show that for a suitable measure which we construct, almost all countable dense sets in the subspaces of piecewise linear functions and of polynomials are Rado. Moreover, all… Expand
1 Citations

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<p>Given a countable dense subset <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S"> <mml:semantics> <mml:mi>S</mml:mi> Expand