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Full-Text Articles in Physical Sciences and Mathematics
Properties Of Functionally Alexandroff Topologies And Their Lattice, Jacob Scott Menix
Properties Of Functionally Alexandroff Topologies And Their Lattice, Jacob Scott Menix
Masters Theses & Specialist Projects
This thesis explores functionally Alexandroff topologies and the order theory asso- ciated when considering the collection of such topologies on some set X. We present several theorems about the properties of these topologies as well as their partially ordered set.
The first chapter introduces functionally Alexandroff topologies and motivates why this work is of interest to topologists. This chapter explains the historical context of this relatively new type of topology and how this work relates to previous work in topology. Chapter 2 presents several theorems describing properties of functionally Alexandroff topologies ad presents a characterization for the functionally Alexandroff topologies …
A Classification Of The Intersections Between Regions And Their Topical Transitions, Kathleen Bell
A Classification Of The Intersections Between Regions And Their Topical Transitions, Kathleen Bell
Mahurin Honors College Capstone Experience/Thesis Projects
As two topological regions are morphed and translated, how does their intersection change? Previous research has been done on static configurations with planar spatial regions. I expand upon this research to include dynamically changing regions and intersections. I examine what forms of intersection are possible, and what transitions are directly possible, while considering such variables as the connectedness of the regions.
Counting The Number Of Locally Convex Topologies On A Totally Ordered Finiate Set, Thomas Tyler Clark
Counting The Number Of Locally Convex Topologies On A Totally Ordered Finiate Set, Thomas Tyler Clark
Mahurin Honors College Capstone Experience/Thesis Projects
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.