Ingram, William T.2022-02-032022-02-03196813678583https://hdl.handle.net/10657/8649Ordered spaces are an abstraction of the real line. This paper shows in Chapter 1 that all ordered spaces are hereditarily normal. In Chapter 2, necessary and sufficient conditions are given for a separable ordered space to be completely separable, and hence metrizable. In semi-metrizable ordered spaces the following are shown to be equivalent: (a) The space is completely separable. (b) The space is separable. (c) The space is hereditarily separable. (d) The space has the Lindelof property. (e) If M is an uncountable subset of the space, then some point of M is a limit point of M. (f) There does not exist an uncountable collection of mutually exclusive open sets in the space.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital