The Tits core G^+ of a totally disconnected locally compact group G is
defined as the abstract subgroup generated by the closures of the contraction
groups of all its elements. We show that a dense subgroup is normalised by the
Tits core if and only if it contains it. It follows that every dense subnormal
subgroup contains the Tits core. In particular, if G is topologically simple,
then the Tits core is abstractly simple, and if G^+ is non-trivial then it is
the unique minimal dense normal subgroup. The proofs are based on the fact, of
independent interest, that the map which associates to an element the closure
of its contraction group is continuous.Comment: 11 page