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Extended by Balk Metrics
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  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 2,  2015, pp.449-472
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.2.449
 Title & Authors
Extended by Balk Metrics
DOVGOSHEY, OLEKSIY; DORDOVSKYI, DMYTRO;
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 Abstract
Let X be a nonempty set and (X) be the set of nonempty finite subsets of X. The paper deals with the extended metrics recently introduced by Peter Balk. Balk`s metrics and their restriction to the family of sets A with make possible to consider "distance functions" with n variables and related them quantities. In particular, we study such type generalized diameters and find conditions under which is a Balk`s metric. We prove the necessary and sufficient conditions under which the restriction to the set of with is a symmetric G-metric. An infinitesimal analog for extended by Balk metrics is constructed.
 Keywords
generalized diameter;G-metric;pretangent space;ultrametric;ultrafilter;
 Language
English
 Cited by
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