This dissertation focuses on two properties considered for bases and π-bases of topological spaces. The first of the discussed properties, introduced by R. Freese and J. B. Nation, was originally considered for lattices. The second property considered by W. Fleissner and L. Yengulalp is related to the domain theory introduced by D. Scott. The results on Freese-Nation properties are presented in Chapters 2-5.
The results for spaces represented by the domain were presented in Chapter 6