We prove the following generalization of Cartwright–Littlewood fixed point theorem. Suppose h : R 2 → is an orientation preserving planar homeomorphism, and X acyclic continuum. Let C be a component ∩ ( ) . If there c ∈ such that O + ⊆ or − then also contains Our result generalizes earlier results Ostrovski Boroński, answers Question from Boroński (2017). The proof inspired by short Cartwright ...