Date of Award:
Master of Science (MS)
Mathematics and Statistics
John E. Kimber, Jr.
The Buoyancy Theorem states that a compact set is buoyant if every point of the compact set has a neighborhood whose intersection with the compact set is buoyant. In this paper, the Buoyancy Theorem is used to prove several standard results involving compact sets. The proof of such a result may be a direct application of the Buoyancy Theorem or the proof may rely on a certain compactness argument which follows from the Buoyancy Theorem. The last application in this paper is such an example.
The method used is to, first of all, define a buoyancy on the compact set; secondly, show that every point of the compact set has a neighborhood whose intersection with the compact set is buoyant; and finally, apply the Buoyancy Theorem to conclude that the compact set is buoyant.
Cutler, Elwyn David, "A Concept of Buoyancy in Topological Spaces, with Applications to the Foundations of Real Variables" (1969). All Graduate Theses and Dissertations. 6824.