  We study the behaviour of Tikhonov regularisation on topological spaces with
multiple regularisation terms. The main result of the paper shows that
multi-parameter regularisation is well-posed in the sense that the results
depend continuously on the data and converge to a true solution of the equation
to be solved as the noise level decreases to zero. Moreover, we derive
convergence rates in terms of a generalised Bregman distance using the method
of variational inequalities. All the results in the paper, including the
convergence rates, consider not only noise in the data, but also errors in the
operator.
