IJPAM: Volume 28, No. 3 (2006)

THE POLYGON CASE OF THE THETA-CURVE THEOREM

Olga Bodroza-Pantic$^1$, Ratko Tošic$^2$, Bogdanka Jakovljev$^3$
$^{1,2}$Department of Mathematics and Informatics
Faculty of Sciences
Trg. D. Obradovica 4, University of Novi Sad
Novi Sad, 21000, SERBIA
$^1$e-mail: bodroza@im.ns.ac.yu
$^2$e-mail: ratosic@im.ns.ac.yu
$^3$Secondary School ``Jovan Vukanovic''
Gagarinova 1, 21000, Novi Sad, SERBIA


Abstract.The well known game of HEX uses the following corollary of the Jordan Curve Theorem, so-called Theta-Curve Theorem: An open Jordan curve with its endpoints on a closed Jordan curve ${\cal K}$, but otherwise located in the bounded part, divides the closure of the bounded part into two parts.

Some students in a honor class, who have not been previously exposed to homology theory, after being motivated by the game of HEX, may be given direct and elementary proofs of the polygon case of both the Jordan Curve Theorem and the Theta-Curve Theorem.

Received: March 21, 2006

AMS Subject Classification: 40D25, 40D05, 51A20

Key Words and Phrases: Jordan curve, neighborhood, interior, boundary

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 28
Issue: 3