# 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} }

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

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