On the property of Kelley for Hausdorff continua

Abstract

We introduce the conceptsHausdorff maximal limit continuumandHausdorff strong maximal limit continuum, for Hausdorff continua; thesedefinitions extend the concepts of maximal limit continuum and strong max-imal limit continuum, respectiveley, introduced by J. J. Charatonik and W.J. Charatonik in 1998 for metric continua [1, Definitions 2.2and 2.3]. Weshow that in metric continua, being a maximal limit continuum is equivalentto being a Hausdorff maximal limit continuum. We also show that in metriccontinua, being a strong maximal limit continuum implies being a Hausdorffstrong maximal limit continuum. Finally, we show an equivalence of havingthe property of Kelley, in terms of these new definitions, whose analog versionfor metric continua was given by J. J. Charatonik and W. J. Charatonik.