Surface Attractors

Let $f$ be a continuous endomorphism of a surface $M$, and $A$ an attracting set such that the restriction $f{\mathrm{\mid }}_A:A\to A$ is a $d:1$ covering map. We show that if $f$ is a local homeomorphism in the immediate basin $B_A^0$ of $A$, then $f$ is also a $d:1$ covering of $B_A^0$.