The use of intrinsic topology such as interval topology and order topology that were typically symmetric was discussed. The theory of continuous lattices provided strong motivation for the consideration of such topologies such as the Scott topology or the hull-kernel topology which were not symmetric. Another approach to the study of topology on ordered structures was to begin with a set X equipped both with a partial order ≤ and a topology. The results show that these orders were called as closed order and the resulting ordered topological space was called as pospace, when the assumption was satisfied.
Publication Source (Journal or Book title)
Electronic Notes in Theoretical Computer Science
Lawson, J. (1998). The upper interval topology, property M, and compactness. Electronic Notes in Theoretical Computer Science, 13, 158-172. https://doi.org/10.1016/S1571-0661(05)80220-8