Surówka, Wojciech A discrete form of Jordan curve theorem. (English) Zbl 0807.52018 Pr. Nauk. Uniw. Śląsk. Katowicach 1399, Ann. Math. Silesianae 7, 57-61 (1993). 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) Cited in 1 ReviewCited in 5 Documents MSC: 52C99 Discrete geometry 54F50 Topological spaces of dimension \(\leq 1\); curves, dendrites Keywords:reduced chessboard theorem; Jordan curve theorem PDFBibTeX XMLCite \textit{W. Surówka}, Pr. Nauk. Uniw. Śląsk. Katowicach, Ann. Math. Silesianae 1399(7), 57--61 (1993; Zbl 0807.52018)