  We develop a cooling method controlled by a physical cooling radius that
defines a scale below which fluctuations are smoothed out while leaving physics
unchanged at all larger scales. We apply this method to study topological
properties of lattice gauge theories, in particular the behaviour of
instantons, dislocations and instanton--anti-instanton pairs. Monte Carlo
results for the SU(2) topology are presented. We find that the method provides
a means to prevent instanton--anti-instanton annihilation under cooling. While
the instanton sizes are largely independent from the smoothing scale, the
density and pair separations are determined by the particular choice made for
this quantity. We discuss the questions this raises for the "physicality" of
these concepts.
