  In this dissertation, we investigate the approach of pure SU(2) lattice gauge
theory to its continuum limit using the deconfinement temperature, six gradient
scales, and six cooling scales. We find that cooling scales exhibit similarly
good scaling behavior as gradient scales, while being computationally more
efficient. In addition, we estimate systematic error in continuum limit
extrapolations of scale ratios by comparing standard scaling to asymptotic
scaling. Finally we study topological observables in pure SU(2) using cooling
to smooth the gauge fields, and investigate the sensitivity of cooling scales
to topological charge. We find that large numbers of cooling sweeps lead to
metastable charge sectors, without destroying physical instantons, provided the
lattice spacing is fine enough and the volume is large enough. Continuum limit
estimates of the topological susceptibility are obtained, of which we favor
$\chi^{1/4}/T_c = 0.643(12)$. Differences between cooling scales in different
topological sectors turn out to be too small to be detectable within our
statistical error.
