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Chris Judge
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Why is a component of complement of Jordan curve 1-connected w/o Sch\"onflies?

The complement of a simple closed curve in the Euclidean plane has two connected components (Jordan). Schoenflies theorem implies that each of these components is homeomorphic to a disk and hence each has trivial fundamental group. Is there a direct (and simple) way to see that each component has trivial fundamental group without invoking Schoenflies?

Chris Judge
  • 494
  • 4
  • 13