We consider certain groups of tree automorphisms as so-called diffeological
groups. The notion of diffeology, due to Souriau, allows to endow non-manifold
topological spaces, such as regular trees that we look at, with a kind of a
differentiable structure that in many ways is close to that of a smooth
manifold; a suitable notion of a diffeological group follows. We first study
the question of what kind of a diffeological structure is the most natural to
put on a regular tree in a way that the underlying topology be the standard one
of the tree. We then proceed to consider the group of all automorphisms of the
tree as a diffeological space, with respect to the functional diffeology,
showing that this diffeology is actually the discrete one, the fact that
therefore is true for its subgroups as well.Comment: 11 pages, 1 figure; rather minor changes with respect to the previous
versio
