Geodesic
Pseudo-homotopies of the pseudo-arc
Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 4, pp. 629-635.

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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.
Classification : 54B10, 54F15, 54F50
Keywords: pseudo-arc; pseudo-contractible; pseudo-homotopy 
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Illanes, Alejandro. Pseudo-homotopies of the pseudo-arc. Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 4, pp. 629-635. http://geodesic.mathdoc.fr/item/CMUC_2012__53_4_a9/