Semi-Kelley continua
Volume 163 / 2021
Abstract
We present an alternative definition to the property of being a semi-Kelley continuum. Using it we are able to extend some results in the literature and to obtain new ones. We give a family of mappings preserving the property of being a semi-Kelley continuum; this family includes retractions, monotone mappings and open mappings. We prove that semi-Kelley continua do not contain -continua. We show that for fans, being semi-Kelley implies semi-smoothness. We also prove that for a continuum X the following are equivalent: (i) X\times [0,1] is semi-Kelley, (ii) {\rm cone}(X) is semi-Kelley, and (iii) {\rm suspension}(X) is semi-Kelley.