Abstract. A generalized metric space (g.m.s) has been defined as a metric space in which the triangle inequality is replaced by the 'Quadrilateral inequal-
Main resultIn what follows N denotes the set of natural numbers. The basic terms are already defined in the abstract. We denote {y ∈ X : d(x, y) < r} for x in a g.m.s (X, d) by B r (x). In [1], the following were taken for granted and used:(1) {B r (x) : r > 0, x ∈ X} is a basis for a topology on X (2) d is continuous in each of the coordinates and (3) a g.m.s is a Hausdorff space. The following examples shows that (1), (2)and (3)
We provide a construction for the completion of a dislocated metric space (abbreviated -metric space); we also prove that the completion of the metric associated with a -metric coincides with the metric associated with the completion of the -metric.
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