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A discrete form of Jordan curve theorem. (English) Zbl 0807.52018

A purely combinatorial argument is used to establish the so-called “Reduced Chessboard Theorem” which, in particular, allows a deduction of a similar statement due to Steinhaus. This last result is then applied to get a new proof of a discrete analogue to the Jordan Curve Theorem.
Reviewer: M.Turinici (Iaşi)

MSC:

52C99 Discrete geometry
54F50 Topological spaces of dimension \(\leq 1\); curves, dendrites
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