The comb representation of compact ultrametric spaces

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• 作者：A. Lambert ; G. Uribe Bravo
• 关键词：Key wordsreal tree ; coalescent ; mass measure ; visibility measure ; local time ; p ; adic field ; coalescent point process
• 刊名：P-Adic Numbers, Ultrametric Analysis, and Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：9
• 期：1
• 页码：22-38
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra;
• 出版者：Pleiades Publishing
• ISSN：2070-0474
• 卷排序：9

文摘

We call a comb a map f: I → [0,∞), where I is a compact interval, such that {f ≥ ε} is finite for any ε > 0. A comb induces a (pseudo)-distance \({\overline d _f}\) on {f = 0} defined by \({\overline d _f}\left( {s,t} \right) = {\max _{\left( {s \wedge t,s \vee t} \right)}}f\). We describe the completion \(\overline I \) of {f = 0} for this metric, which is a compact ultrametric space called the comb metric space.