In this paper we consider rational subspaces of the plane. A rational space is a space which has a basis of open sets with countable boundaries. In the special case where the boundaries are finite, the space is called rim-finite.

Let $X$ be a continuum. Two maps $g,h:X\to X$ are said to be pseudo-homotopic provided that there exist a continuum $C$, points $s,t\in C$ and a continuous function $H:X\times C\to X$ such that for each $x\in X$, $H(x,s)=g\left(x\right)$ and $H(x,t)=h\left(x\right)$. In this paper we prove that if $P$ is the pseudo-arc, $g$ is one-to-one and $h$ is pseudo-homotopic to $g$, then $g=h$. This theorem generalizes previous results by W. Lewis and M. Sobolewski.