Remarks on Homotopies Associated With Khalimsky Topology

Abstract

Abstract. Several kinds of homotopies have been substantially used to study topological properties of digital spaces. The present paper, as a survey article, studies some recent results in the field of homotopy theory associated with Khalimsky topology. In particular, Khalimsky topological properties of digital products related to the establishment of the homotopies are mainly treated.

Topological graphs based on a new topology on Zn and its applications

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Up to now there is no homotopy for Marcus-Wyse (for short M-) topological spaces. In relation to the development of a homotopy for the category of Marcus-Wyse (for short M-) topological spaces on Z 2 , we need to generalize the M-topology on Z 2 to higher dimensional spaces X ⊂ Z n , n ≥ 3 [18]. Hence the present paper establishes a new topology on Z n , n ∈ N, where N is the set of natural numbers.

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