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Subjects
54-XX General topology
54Cxx Maps and general types of spaces defined by maps
54C10 Special maps on topological spaces (open, closed, perfect, etc.)

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Property Q.

Bandy, C. (1991)

International Journal of Mathematics and Mathematical Sciences

Pseudo-homotopies of the pseudo-arc

Alejandro Illanes (2012)

Commentationes Mathematicae Universitatis Carolinae

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 $x \in X$ , $H (x, s) = g (x)$ 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.

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