Soft isomorphism for digital images and computational topological applications

Abstract

In this paper the concept of soft continuity is focused on for digital images by using soft sets which is defined on κ - adjacent digital images. Also the definitions of digital soft isomorphism and digital soft retraction are given. Some theorems are obtained deal with soft isomorphism and soft retraction for digital images and some numerical examples are presented in dimension 2. Finally digital soft retraction is obtained as a soft topological invariant.

Soft super-continuity and soft delta-closed graphs

“…For instance, “soft semi-continuous” [ 40 ], “soft pre-continuous” [ 27 ], “soft β -continuous” [ 41 ], “soft θ -continuous” [ 26 ], “soft α -continuous” [ 27 ], “soft δ -continuous” [ 30 ], “soft ω -continuous” [ 42 ], “soft ω s -continuous” [ 42 ], “weakly soft β -continuous” [ 35 ], “weakly soft pre-continuous” [ 36 ], “weakly soft α -continuous” [ 38 ], “soft complete continuous” [ 43 ], “soft strongly continuous” [ 43 ], “soft C -continuous” [ 44 ], “soft almost C -continuous” [ 44 ], “soft ω - θ -continuous” [ 45 ], “soft weakly θ ω -continuous” [ 45 ], and so on. The authors in [ 46 ] proved that soft continuity is useful in developing computational topological applications and digital images.…”

Some Classes of Soft Functions Defined by Soft Open Sets Modulo Soft Sets of the First Category

“…In addition to soft topology, soft continuity is useful in the development of computational topological applications and digital images [24]. Soft continuity of functions was defined by Zorlutuna et al [25] in 2012.…”