Title

Relationships between Hereditary Sobriety, Sobriety, TD, T1, and Locally Hausdorff

Author(s)

Stephen Rodabaugh, Youngstown State UniversityFollow
Jeffrey T. Denniston, Kent State UniversityFollow
Austin Melton, Kent State UniversityFollow
Jamal K. Tartir, Youngstown State UniversityFollow

Document Type

Topology + Asymmetric Structures

Publication Date

6-2017

Publication Source

32nd Summer Conference on Topology and Its Applications

Abstract

This work augments the standard relationships between sobriety, T₁, and Hausdorff by mixing in locally Hausdorff and the compound axioms sober + T₁ and sober + T_D. 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.

Comments

This document is available for download with the permission of the presenting author and the organizers of the conference. Permission documentation is on file.

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Copyright

Copyright © 2017, the Authors

eCommons Citation

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.
https://ecommons.udayton.edu/topology_conf/54