# The Jordan Curve Theorem, Formally and Informally

@article{Hales2007TheJC, title={The Jordan Curve Theorem, Formally and Informally}, author={Thomas C. Hales}, journal={The American Mathematical Monthly}, year={2007}, volume={114}, pages={882 - 894} }

1. INTRODUCTION. The Jordan curve theorem states that every simple closed pla-nar curve separates the plane into a bounded interior region and an unbounded exterior. One hundred years ago, Oswald Veblen declared that this theorem is " justly regarded as a most important step in the direction of a perfectly rigorous mathematics " [13, p. 83]. Its position as a benchmark of mathematical rigor has continued to our day. Many vastly underestimate the logical gulf that separates a typical published…

## 116 Citations

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