Completely regular ordered spaces
This paper studies a concept introduced in a not yet published paper of \textit{J. D. Lawson}: a strictly completely regular (partially) ordered space. The definition is long; it is said to be equivalent to a definition in a 1968 Edinburgh dissertation by \textit{M. J. Canfell}. Lawson showed that these spaces are completely regular ordered in the sense of \textit{L. Nachbin} [Topology and Order (1965; Zbl 0131.379)], and asked if the converse is true. The author shows that it is not true. However, it becomes true if the space is required to be locally compact, or a topological lattice, or a C-space (i.e. the smallest upper set containing a closed set is closed, and also the smallest lower set containing it).
scientific article; zbMATH DE number 4205376
scientific article