  We present a general method for solving the non--linear differential equation
of monotonically increasing steady--state radiation driven winds. We
graphically identify all the singular points before transforming the momentum
equation to a system of differential equations with all the gradients
explicitly give. This permits a topological classification of all singular
points and to calculate the maximum and minimum mass--loss of the wind. We use
our method to analyse for the first time the topology of the non--rotating
frozen in ionisation m--CAK wind, with the inclusion of the finite disk
correction factor and find up to 4 singular points, three of the x--type and
one attractor--type. The only singular point (and solution passing through)
that satisfies the boundary condition at the stellar surface is the standard
m--CAK singular point.
