The product of two chainable Kelley continua is also a Kelley continuum

For many years, it was an open question whether the product of two Kelley continua is also a Kelley continuum. In 1977, Roger W. Wardle presented a Kelley continuum X such that X x X is not a Kelley continuum. Many years later, in 2004, Janusz J. Charatonik and Wlodzimierz J. Charatonik presented a Kelley continuum X such that X x [0, 1] is not a Kelley continuum. In this paper we prove that the product of two chainable Kelley continua is also a Kelley continuum. (C) 2019 Elsevier B.V. All rights reserved.