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A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.
16
votes
Groups acting on trees
The case of actions on trees is a useful motivating baby case illustrating the above "classification"; all cases can actually occur. …
11
votes
Accepted
Embedding of real trees into $\ell_1(\Gamma)$
It's true: there's an isometric embedding of every real tree $T$ on some $\ell^1$-space, i.e., a set $A$ and a map $f:T\to \ell^1(A)$ that is an isometric embedding, that is, satisfies $\|f(x)-f(x')\| …