Compactifications and property of Kelley in generalized inverse limits - Islas, C; Leonel, R; Tymchatyn, E. D. (Topology Proceedings, 2021)
To the memory of Phil Zenor: A fine mathematician who enjoyed a full life and who brightened the lives of those around him. In 1969, R. Bennett gave conditions on a continuous function f:[0,1] →[0,1] so the inverse limit X with fixed bonding map f is the compactification of a ray. Mahavier in 2004 relaxed the continuity assumption on f to upper semicontinuous and continuum-valued to show X is a compactification of a connected set R. We generalize Mahavier’s result and give necessary and sufficient conditions for R to be a ray. We also give conditions so X has the property of Kelley if X R does. These results partially answer questions posed by W. T. Ingram in 2012.