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Hereditarily non-weakly chainable continua in products of plane continua

Volume 239 / 2017

Alejandro Illanes Fundamenta Mathematicae 239 (2017), 19-27 MSC: Primary 54F15; Secondary 54B10, 54F50. DOI: 10.4064/fm315-10-2016 Published online: 28 March 2017

Abstract

We prove that the product of any two non-degenerate plane continua contains a non-degenerate hereditarily non-weakly chainable continuum. Consequently, in the product of two pseudo-arcs, there exists a non-degenerate subcontinuum containing no pseudo-arc. This answers a question by D. P. Bellamy.

Authors

  • Alejandro IllanesInstituto de Matemáticas
    Universidad Nacional Autónoma de México
    Circuito Exterior, Cd. Universitaria
    04510, México, D.F., Mexico
    and
    Department of Mathematics
    Texas Tech University
    Lubbock, Texas 79409-1042, U.S.A.
    e-mail

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