Two Topological Uniqueness Theorems for Spaces of Real Numbers
@article{Francis2012TwoTU,
title={Two Topological Uniqueness Theorems for Spaces of Real Numbers},
author={M. D. Francis},
journal={arXiv: General Topology},
year={2012}
}A 1910 theorem of Brouwer characterizes the Cantor set as the unique totally disconnected, compact metric space without isolated points. A 1920 theorem of Sierpinski characterizes the rationals as the unique countable metric space without isolated points. The purpose of this exposition is to give an accessible overview of this celebrated pair of uniqueness results. It is illuminating to treat the problems simultaneously because of commonalities in their proofs. Some of the more counterintuitive…
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