Abstract: In this paper the author studies the boundary behavior of μ(z)-homeomorphisms. A sufficient condition is given such that the μ(z)-homeomorphism of the upper half plane onto itself can be topologically extended to the boundary. The auther also estimates the ρ-function by the dilatation function of μ(z)-homeo morphism.

Key words: Beltrami equation, Quasiconformal mapping, μ(z)-homeomorphism,
ρ-function, Dilatation function