The classical Jordan curve theorem (JCT) says,

Every Jordan curve (a non-self-intersecting continuous loop in the plane) separates the plane into exactly two components.

It is often mentioned just in passing in courses ranging from liberal arts mathematics courses, where it is an illuminating example of an “obvious” statement that is difficult to prove, to undergraduate and graduate topology and complex analysis, where it tends to break the flow. In complex analysis, it is especially given short shrift. There are several reasons for this short shrift. For one, a professor has bigger fish to fry. There are the theorems of

EP - 129 PB - Princeton University Press PY - 2014 SN - 9780691160412 SP - 120 T2 - The Best Writing on Mathematics 2013 UR - http://www.jstor.org/stable/j.ctt4cgb74.16 Y2 - 2020/09/18/ ER -