Vol. 2, No. 3, 2009

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Applications of full covers in real analysis

Karen Zangara and John Marafino

Vol. 2 (2009), No. 3, 297–304

In this paper we briefly introduce the reader to the concept of full covers and indicate how it can be used to prove theorems in an undergraduate analysis course. The technique exposes the student to the idea of covering an interval [a,b] with a collection of sets and then extracting from this collection a subcollection that partitions [a,b]. As a consequence, the student is furnished with a unifying thread that ties together and simplifies the proofs of many theorems.

full covering, partitions, real analysis
Mathematical Subject Classification 2000
Primary: 26A03, 26A06, 26A15, 26A24
Received: 22 August 2008
Accepted: 19 March 2009
Published: 3 October 2009

Communicated by David Larson
Karen Zangara
One Greentree Centre
Suite 201
Marlton, NJ 08053
United States
John Marafino
Department of Mathematics and Statistics
305 Roop Hall, MSC 1911
James Madison University
Harrisonburg, VA 22807
United States