This book introduces oriented version of metrics and cuts and their
multidimensional analogues, as well as partial metrics and weighted
metrics. It is a follow-up of Geometry of Cuts and Metrics by Deza
and Laurent which presents rich theory of classical binary and
symmetric objects - metrics and cuts.Many research publications on
this subject are devoted to different special aspects of the theory
of generalized metrics. However, they are disconnected one from
other, often written in different mathematical language, consider
the same objects from different points of view without analysis of
possible connections, etc. In this book we will construct full
theory of main classes of finite generalized metrics and their
polyhedral aspects.
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