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The Jordan curve theorem and the Schönflies theorem in weak second-order arithmetic

✍ Scribed by Nobuyuki Sakamoto; Keita Yokoyama

Publisher
Springer
Year
2007
Tongue
English
Weight
287 KB
Volume
46
Category
Article
ISSN
0933-5846

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The coverse of the Jordan Curve Theorem
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We show that a compact set F in the plane R 2 is the union of boundaries of a map if and only if each point of F is on the boundary of at least two arcwise connected components of R2\F, and it is accessible from each of those components.

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