Revista Integración (Jan 2020)
On the property of Kelley for Hausdorff continua
Abstract
We introduce the concepts Hausdorff maximal limit continuum and Hausdorff strong maximal limit continuum, for Hausdorff continua; these definitions extend the concepts of maximal limit continuum and strong maximal limit continuum, respectiveley, introduced by J. J. Charatonik and W. J. Charatonik in 1998 for metric continua [1, Definitions 2.2 and 2.3]. We show that in metric continua, being a maximal limit continuum is equivalent to being a Hausdorff maximal limit continuum. We also show that in metric continua, being a strong maximal limit continuum implies being a Hausdorff strong maximal limit continuum. Finally, we show an equivalence of having the property of Kelley, in terms of these new definitions, whose analog version for metric continua was given by J. J. Charatonik and W. J. Charatonik.
