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

Scale Setting and Topological Observables in Pure SU(2) LGT