Extended by Balk Metrics

Let X be a nonempty set and mathcal F(X) be the set of nonempty finite subsets of X. The paper deals with the extended metrics τ : F(X)→ R recently introduced by Peter Balk. Balk's metrics and their restriction to the family of sets A with |A| n make possible to consider "distance functions" with n variables and related them quantities. In particular, we study such type generalized diameters diam tn and find conditions under which B ↦ diam τn B is a Balk's metric. We prove the necessary and sufficient conditions under which the restriction τ to the set of A ∈ F(X) with |A| 3 is a symmetric G-metric. An infinitesimal analog for extended by Balk metrics is constructed. KCI Citation Count: 0