Characterizing indecomposable plane continua from their complements

Details Characterizing indecomposable plane continua from their complements Characterizing indecomposable plane continua from their complements

2008-05-21

arxiv.org/abs/0805.3320v1

Proceedings of the American Mathematical Society. Volume 136, Number 11, November 2008, Pages 4045--4055.

Mathematics

General Topology

11 pages, 3 figures. To appear in Proceedings of the American Mathematical Society

Scientific paper

We show that a plane continuum X is indecomposable iff X has a sequence (U_n) of not necessarily distinct complementary domains satisfying what we call the double-pass condition: If one draws an open arc A_n in each U_n whose ends limit into the boundary of U_n, one can choose components of U_n minus A_n whose boundaries intersected with the continuum (which we call shadows) converge to the continuum.

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