Factorwise rigidity of embeddings of products of pseudo-arcs

Volume 128 / 2012

Mauricio E. Chacón-Tirado, Alejandro Illanes, Rocío Leonel Colloquium Mathematicum 128 (2012), 7-14 MSC: Primary 54F15; Secondary 54B10, 54F50, 55R70. DOI: 10.4064/cm128-1-2

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 $X\times Y$ 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).

Authors

  • Mauricio E. Chacón-TiradoInstituto de Matematicas
    Universidad Nacional Autónoma de México
    Circuito Exterior, Cd. Universitaria
    México 04510, D.F., México
    e-mail
  • Alejandro IllanesInstituto de Matematicas
    Universidad Nacional Autónoma de México
    Circuito Exterior, Cd. Universitaria
    México 04510, D.F., México
    e-mail
  • Rocío LeonelInstituto de Matematicas
    Universidad Nacional Autónoma de México
    Circuito Exterior, Cd. Universitaria
    México 04510, D.F., México
    e-mail

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