• 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… 
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References

SHOWING 1-7 OF 7 REFERENCES
COUNTABLE METRIC SPACES WITHOUT ISOLATED POINTS
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
The Goettingen State and University Library provides access to digitized documents strictly for noncommercial educational, research and private purposes and makes no warranty with regard to their use
Über nulldimensionale Punktmengen
The Topological Characterisation of an Open Linear Interval
On the topological characterization of the real line
On the structure of perfect sets of points