• Corpus ID: 119236370

# 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}
}
• M. Francis
• Published 3 October 2012
• Mathematics
• arXiv: General Topology
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…
1 Citations
Topological models of arithmetic
• Mathematics
• 2018
Ali Enayat had asked whether there is a nonstandard model of Peano arithmetic (PA) that can be represented as $\langle\mathbb{Q},\oplus,\otimes\rangle$, where $\oplus$ and $\otimes$ are continuous

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The theorem is remarkable, and gives some apparently counter-intuitive examples of spaces homeomorphic to the usual Q. Consider the “Sorgenfrey topology on Q,” which has the collection {(p, q] : p, q
Beiträge zur Begründung der transfiniten Mengenlehre
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