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Pseudo-homotopies of the pseudo-arc

Alejandro Illanes (2012)

Commentationes Mathematicae Universitatis Carolinae

Let X be a continuum. Two maps g , h : X X are said to be pseudo-homotopic provided that there exist a continuum C , points s , t C and a continuous function H : X × C X such that for each x 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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