Extremal structure of convex sets

Author

• J. C. Hankins

Abstract

"Let X be a locally compact closed convex subset of a locally convex Haus Dorff topological linear space E. It is shown that every exposed point, respectively, ray of Xis a strongly exposed point, respectively, ray of X. Also, every extreme point, respectively, ray of Xis a denting point, respectively, ray of X. When the above results are combined one can restate two well-known Krein Milman type theorems due to Klee. There exists a closed convex set that has an extreme point that is neither a denting point nor an exposed point.

In Banach spaces, necessary and sufficient conditions are given for the Radon-Nikodym property"-- Abstract, p. ii

Advisor(s)

Rakestraw, Roy M.

Committee Member(s)

Haddock, Glen
Pursell, Lyle E., 1926-2015
Hicks, Troy L.
Robertson, B. Ken

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

1976

Pagination

iv, 52 pages

Note about bibliography

Includes bibliographical references (pages 49-51)

Rights

© 1976 J. C. Hankins, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 4097

Print OCLC #

5985327

Recommended Citation

Hankins, J. C., "Extremal structure of convex sets" (1976). Doctoral Dissertations. 414.
https://scholarsmine.mst.edu/doctoral_dissertations/414