Factorwise rigidity of embeddings of products of pseudo-arcs

@article{MauricioE2012,
abstract = {An embedding from a Cartesian product of two spaces into the Cartesian product of two spaces is said to be factorwise rigid provided that it is the product of embeddings on the individual factors composed with a permutation of the coordinates. We prove that each embedding of a product of two pseudo-arcs into itself is factorwise rigid. As a consequence, if X and Y are metric continua with the property that each of their nondegenerate proper subcontinua is homeomorphic to the pseudo-arc, then X × Y is factorwise rigid. This extends results of D. P. Bellamy and J. M. Lysko (for the case that X and Y are pseudo-arcs) and of K. B. Gammon (for the case that X is a pseudo-arc and Y is either a pseudo-circle or a pseudo-solenoid).},
author = {Mauricio E. Chacón-Tirado, Alejandro Illanes, Rocío Leonel},
journal = {Colloquium Mathematicae},
keywords = {embedding; factorwise rigid product; factorwise rigid embedding; pseudo-arc; pseudo-circle; pseudo-solenoid},
language = {eng},
number = {1},
pages = {7-14},
title = {Factorwise rigidity of embeddings of products of pseudo-arcs},
url = {http://eudml.org/doc/283990},
volume = {128},
year = {2012},
}

TY - JOUR
AU - Mauricio E. Chacón-Tirado
AU - Alejandro Illanes
AU - Rocío Leonel
TI - Factorwise rigidity of embeddings of products of pseudo-arcs
JO - Colloquium Mathematicae
PY - 2012
VL - 128
IS - 1
SP - 7
EP - 14
AB - An embedding from a Cartesian product of two spaces into the Cartesian product of two spaces is said to be factorwise rigid provided that it is the product of embeddings on the individual factors composed with a permutation of the coordinates. We prove that each embedding of a product of two pseudo-arcs into itself is factorwise rigid. As a consequence, if X and Y are metric continua with the property that each of their nondegenerate proper subcontinua is homeomorphic to the pseudo-arc, then X × Y is factorwise rigid. This extends results of D. P. Bellamy and J. M. Lysko (for the case that X and Y are pseudo-arcs) and of K. B. Gammon (for the case that X is a pseudo-arc and Y is either a pseudo-circle or a pseudo-solenoid).
LA - eng
KW - embedding; factorwise rigid product; factorwise rigid embedding; pseudo-arc; pseudo-circle; pseudo-solenoid
UR - http://eudml.org/doc/283990
ER -