High Quality Content by WIKIPEDIA articles! A geodesic metric space X is called tree-graded with respect to a collection of connected proper subsets (called pieces) if any two distinct pieces intersect by at most one point, and every non-trivial simple geodesic triangle of X is contained in one of the pieces. In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space. In fact, the notion of "metric" is a generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight line connecting them.

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