Date of Award
Master of Science (MS)
The primary purpose of this thesis is to construct a topology on the collection of maximal ideals of a distributive and complemented lattice using the hull-kernel methodology. Through the construction of this topological space, we discovered that the space is compact, zero-dimensional, and Hausdorff. Next, we looked at the properties of some lattices, namely the power set of a finite set ordered by inclusion and the set of all positives divisors for some arbitrary integer ordered by divisibility. Whenever these lattices were both distributive and complemented, we constructed a topology on the collection of maximal ideals of the lattices using the hull-kernel methodology. Finally, we applied our prior results to these topological spaces to help us further understand the structure of a topological space constructed using this methodology.
Boolean algebra, lattice, order theory, poset
Number of Pages
University of South Dakota
Moos, Abbigal, "Explorations of a Topology Constructed on the Maximal Ideals of a Boolean Algebra" (2023). Dissertations and Theses. 130.