We look at locally convex topologies on a totally ordered finite set. We determine a method of finding an upper bound on the number of such topologies on an n element. We show how this problem is related to Pascal's Triangle and the Fibonacci Numbers. We explain an algorithm for determining the number of locally convex topologies consisting of nested intervals.
Advisor(s) or Committee Chair
Dr. Tom Richmod
Mathematics | Physical Sciences and Mathematics
Clark, Thomas Tyler, "Counting the Number of Locally Convex Topologies on a Totally Ordered Finiate Set" (2010). Honors College Capstone Experience/Thesis Projects. Paper 226.