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property: a real tree is simplicial if and only if the set of singular points of (points whose complement in has three or more connected components) is closed and discrete in .
* The -tree obtained in the following way is nonsimplicial. Start with the interval [0, 2] and glue, for each positive integer n, an interval of length 1/n to the point 1 - 1/n in the original interval. The set of singular points is discrete, but fails to be closed since 1 is an ordinary point in this -tree. Gluing an interval to 1 would result

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