Jordan Areas and Grids

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Abstract

Jordan curves can be used to represent special subsets of the Euclidean plane, either the (open) interior of the curve or the (compact) union of the interior and the curve itself. We compare the latter with other representations of compact sets using grids of points and we are able to show that knowing the length of a rectifiable curve is sufficient to translate from the grid representation to the Jordan curve.

Keywords

representations of compact sets
Jordan curves
Jordan-Schoenflies theorem
TTE

Cited by (0)

1

Research was partially supported by the DFG project 446 CHV 113/240/0-1

2

Research was partially supported by the NSFC projects under Grant No. 60573011, 10410638 and a MOE project under grant number 05JJD72040122