Home > Analysis, Topology > Generalized Jordan Curve Theorem

Generalized Jordan Curve Theorem

If A \subset \Bbb{R}^n is homeomorphic to S^{n-1}, then \Bbb{R}^n \setminus A has two components, and A is the boundary of each.

Generalized Jordan Curve Theorem

For the case n=2 you can find the solution in the following article: Jordan Curve Theorem bidimensional case

Categories: Analysis, Topology Tags: ,
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