Метрична розмірність прямої суми та прямого добутків метричних просторів

Abstract

For an arbitrary metric space (X, d) subset A \subset X is called resolving if for any two points x \ne y \in X there exists point a in subset A for which following inequality holds d(a, x) \ne d(a, y). Cardinality of the subset A with the least amount of points is called metric dimension. In general, the problem of finding metric dimension of a metric space is NP–hard [1]. In this paper metric dimension for particular constructs of metric spaces is provided. In particular, it is fully characterized metric dimension for the direct sum of metric spaces and shown some properties of the metric dimension of direct product.