Probably the author means a set on which is defined both a metric, making it a metric space, and a group operation, making it a group; and such that the two structures are compatible: the group operation is continuous relative to the topology generated by the metric. In other words: a topolgical group whose topology is generated by a metric.
Probably the author means a set on which is defined both a metric, making it a metric space, and a group operation, making it a group; and such that the two structures are compatible: the group operation is continuous relative to the topology generated by the metric. In other words: a topolgical group whose topology is generated by a metric.
You can see the publication
"About a de nition of metric over an abelian linearly ordered group"
Bice Cavallo, Livia D’Apuzzo
University Federico II, Naples, Italy
Hi
A Metric Group is a built-in or user-defined collection of Metrics, along with some metadata describing the group. Every Metric Group includes an array of metric hashes. The array of metric hashes must have at least one element. In fact, a Metric Group is an object characterized by a hash
For more information visit ""http://dev.copperegg.com/""
Mahmood,
interesting that scientific terminology can be so ambiguous. However, if you take a look to the link which comes with the question, you will find Richard's interpretation to be the relevant one here.
In addition to what has already been cogently observed by others in this thread, you may find the following thesis helpful:
C. Laumann, An idealistic formalization of Stokes' theorem: Pedagogical math in Isabelle/ISAR, M.Sc. thesis, University of Edinburgh, 2004:
http://www.inf.ed.ac.uk/publications/thesis/online/IM040231.pdf
See page 29 for a method that can be used to put together a framework in defining a metric group.
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