Date of Award:

1969

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Advisor/Chair:

John E. Kimber, Jr.

Abstract

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.

Included in

Mathematics Commons

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