Doctoral Dissertations

Abstract

"Elementary length topologies defined on normed and pseudo-normed linear spaces are studied. It is shown that elementary length topologies constructed with different pseudo-norms are never equivalent. Elementary length topologies are constructed on certain topological spaces and some of their properties are investigated. It is shown that certain "measuring devices" (i.e., norms, pseudo-norms, semi-norms, and pseudo-metrics) which take their values in Tikhonov semifields may be used to construct elementary length topologies on any topological linear space. Relationships between two elementary length topologies generated with different measuring devices are considered.

Let (X,t) be a topological linear space such that t is determined from a convex functional, p-norm or quasi-norm. The function q may be used to construct an elementary length topology on X. Let Xr denote X with this elementary length topology and let C(Xr,k) be the set of all bounded, continuous, complex valued functions defined on Xr. Some of the properties of C(Xr,k) which may be used in a quantum mechanical scattering analysis involving elementary length are considered"--Abstract, page ii.

Advisor(s)

Penico, Anthony J., 1923-2011

Committee Member(s)

Plummer, O. R.
Haddock, Glen
Tefft, Wayne E., 1929-1973
Hicks, Troy L.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

1972

Pagination

iv, 53 pages

Note about bibliography

Includes bibliographical references (page 52).

Rights

© 1972 Jackie Ray Hamm, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Library of Congress Subject Headings

Topological spaces
Normed linear spaces
Functional analysis

Thesis Number

T 2786

Print OCLC #

6037007

Electronic OCLC #

904438955

Included in

Mathematics Commons

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