  In this paper, genus statistics have been applied to an HI column density map
of the Small Magellanic Cloud in order to study its topology. To learn how
topology changes with the scale of the system, we provide the study of topology
for column density maps at varying resolution. To evaluate the statistical
error of the genus we randomly reassign the phases of the Fourier modes while
keeping the amplitudes. We find, that at the smallest scales studied ($40
{pc}\leq\lambda\leq 80 {pc}$) the genus shift is in all regions negative,
implying a clump topology. At the larger scales ($110 {pc}\leq\lambda\leq 250
{pc}$) the topology shift is detected to be negative in 4 cases and positive
(``swiss cheese'' topology) in 2 cases. In 4 regions there is no statistically
significant topology shift at large scales.
