A Work On Bitopologies Associated With Knots

Authors : Ferit YALAZ, Tamer UĞUR, Ceren Sultan ELMALI

Pages : 2105-2119

Doi:10.21597/jist.1278267

View : 78 | Download : 34

Publication Date : 2023-09-01

Article Type : Research Paper

Abstract :The bitopologies have been associated with some knots in the literature with the help of a method called the knot digraph notation. The knot graphs and quasi pseudo metric spaces were used to obtain these bitopologies. With the help of quasi pseudo metrics, two topologies were obtained on a set. In this way, an association between some knots and bitopologies was established. The authors sought an answer to the question “Given the bitopologies associated with knots, can the knot itself be obtained ?” and they gave a method. This mentioned method consists of 6 steps.. In this work, it is shown in detail that according to the Alexander-Briggs notation, the reverse of the knot digraph notation is provided for the knots 3insert ignore into journalissuearticles values(1);, 5insert ignore into journalissuearticles values(1);, 5insert ignore into journalissuearticles values(2);, 6insert ignore into journalissuearticles values(1);, 6insert ignore into journalissuearticles values(2);, 7insert ignore into journalissuearticles values(1);, 7insert ignore into journalissuearticles values(2);, 7insert ignore into journalissuearticles values(3);, 8insert ignore into journalissuearticles values(1);, 8insert ignore into journalissuearticles values(2);, 8insert ignore into journalissuearticles values(3);, 9insert ignore into journalissuearticles values(1);, 9insert ignore into journalissuearticles values(2);, 9insert ignore into journalissuearticles values(3);, 10insert ignore into journalissuearticles values(1);, 10insert ignore into journalissuearticles values(2);, 10insert ignore into journalissuearticles values(3);.
Keywords : Düğüm, Digraf, Bitopoloji, Zayıf Küme, Güçlü Küme

ORIGINAL ARTICLE URL