  Using Monte Carlo simulations with overrelaxation, we have equilibrated
lattices up to $\beta=2.928$, size $60^4$, for pure SU(2) lattice gauge theory
with the Wilson action. We calculate topological charges with the standard
cooling method and find that they become more reliable with increasing $\beta$
values and lattice sizes. Continuum limit estimates of the topological
susceptibility $\chi$ are obtained of which we favor
$\chi^{1/4}/T_c=0.643\,(12)$, where $T_c$ is the SU(2) deconfinement
temperature. Differences between cooling length scales in different topological
sectors turn out to be too small to be detectable within our statistical
errors.
