2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107560This paper has been withdrawn by the author. The author found that the main results here were already obtained by K. Taniyama and A. Yasuhara `On $C$-distance of knots. Kobe J. Math. 11 (1994), no. 1, 117--127. MR1309997 (95j:57010)'. He would like to thank M. Ozawa for the information.This paper has been withdrawnGeometric Topology57M25Surface distance on knotstext