Arithmetic continuity in cone metric space

William Henry Ruckle introduced the notion of arithmetic convergence in the sense that a sequence defined on the set of natural numbers is said to be arithmetic convergent if for each there is an integer such that for every integer , , where denotes the greatest common divisor of m and n. In this paper, the notion of arithmetic convergence has been extended to cone metric space. Using the concept of arithmetic convergence, arithmetic continuity and arithmetic compactness have been defined in cone metric spaces and give some interesting results.