A chordal filling is the closed connected set obtained from a proper boundary-to-boundary path by adding complementary pockets disconnected from both boundary arcs between its marked endpoints. In it meets the boundary only at zero and infinity and leaves two complementary simply connected sides, adjacent to the negative and positive real axes. Equivalently it is full with respect to the two marked boundary arcs. This definition uses the prime ends of a general simply connected domain and is preserved by conformal maps.
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