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Results tagged with terminology
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user 22833
Questions of the kind "What's the name for a X that satisfies property Y?"
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Mapping in reference to a metric space (terminology question)
I'm not certain that all of the conditions you mention in your "definition" are satisfied in this setting, but I think you should look at $\Gamma$-Ultrametric spaces, c.f. notes by Ackerman, where $\G …
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