Topology + Asymmetric Structures
32nd Summer Conference on Topology and Its Applications
This work augments the standard relationships between sobriety, T1, and Hausdorff by mixing in locally Hausdorff and the compound axioms sober + T1 and sober + TD. We show the latter compound condition characterizes hereditary sobriety, and that locally Hausdorff fits strictly between Hausdorff and sober + T1. Classes of examples are constructed, in part to show the non-reversibility of key implications.
Copyright © 2017, the Authors
Rodabaugh, Stephen; Denniston, Jeffrey T.; Melton, Austin; and Tartir, Jamal K., "Relationships between Hereditary Sobriety, Sobriety, TD, T1, and Locally Hausdorff" (2017). Summer Conference on Topology and Its Applications. 54.