Abstract:Let $X$ be a continuum. Two maps $g,h:X\rightarrow X$ are said to be pseudo-homotopic provided that there exist a continuum $C$, points $s,t\in C$ and a continuous function $H:X\times C\rightarrow X$ such that for each $x\in X$, $H(x,s)=g(x)$ and $H(x,t)=h(x)$. 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.
Keywords: pseudo-arc, pseudo-contractible, pseudo-homotopy
AMS Subject Classification: 54F15 54B10 54F50