Pseudo-homotopies of the pseudo-arc

Illanes, Alejandro. "Pseudo-homotopies of the pseudo-arc." Commentationes Mathematicae Universitatis Carolinae 53.4 (2012): 629-635. <http://eudml.org/doc/252524>.

@article{Illanes2012,
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.},
author = {Illanes, Alejandro},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {pseudo-arc; pseudo-contractible; pseudo-homotopy; pseudo-arc; pseudo-contractible; pseudo-homotopy},
language = {eng},
number = {4},
pages = {629-635},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Pseudo-homotopies of the pseudo-arc},
url = {http://eudml.org/doc/252524},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Illanes, Alejandro
TI - Pseudo-homotopies of the pseudo-arc
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 4
SP - 629
EP - 635
AB - 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.
LA - eng
KW - pseudo-arc; pseudo-contractible; pseudo-homotopy; pseudo-arc; pseudo-contractible; pseudo-homotopy
UR - http://eudml.org/doc/252524
ER -