Publishing house / Journals and Serials / Colloquium Mathematicum / All issues

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 $R^{3}$-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.