A Generalization of a Theorem of Weierstrass

Local homeomorphisms satisfying generalized modular inequalities

“…As in Theorem 2 we can prove an extension of the well known theorem of Zoric [43] and of some theorems of Agard and Marden [44] and Cristea [6] and we give some partial extensions of some results of Rajala [22] and Cristea [9]. It is known that Zoric's theorem does not hold in the case n = 2 as the function exp: C → C shows.…”

“…differentiable and satisfy condition (N ). Using Sard's lemma from [39], we see that in this case f is a.e. differentiable and J f (x) = 0 a.e.…”

“…Since f is a local homeomorphism on D r , we can use the univalence on the border theorem from [39] to see that f |D r : B(z, s), D r ⊂ D s and we reached a contradiction. We can suppose that Card (D r ∩ C) = 1 for 0 < r < r 0 and let c ∈ C be such that lim x→c f (x) = ∞ and f is a local homeomorphism on R n \ {c}.…”