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Semitopological Groups
This thesis is a study of semitopological groups, a similar but weaker notion than that of topological groups. It is shown that all topological groups are semitopological groups but that the converse is not true. This thesis investigates some of the conditions under which semitopological groups are, in fact, topological groups. It is assumed that the reader is familiar with basic group theory and topology.
Date:
December 1971
Creator:
Scroggs, Jack David
System:
The UNT Digital Library
Completeness Axioms in an Ordered Field
The purpose of this paper was to prove the equivalence of the following completeness axioms. This purpose was carried out by first defining an ordered field and developing some basic theorems relative to it, then proving that lim [(u+u)*]^n = z (where u is the multiplicative identity, z is the additive identity, and * indicates the multiplicative inverse of an element), and finally proving the equivalence of the five axioms.
Date:
December 1971
Creator:
Carter, Louis Marie
System:
The UNT Digital Library
The Fundamental Group of Certain Toplogical Spaces
The problem confronted in this thesis is that of determining direct calculations of the fundamental group of certain topological spaces.
Date:
December 1971
Creator:
Hopkins, Billy L.
System:
The UNT Digital Library
Inequalities and Set Function Integrals
This thesis investigates some inequalities and some relationships between function properties and integral properties.
Date:
December 1971
Creator:
Milligan, Kenneth Wayne
System:
The UNT Digital Library
Uniform Locally Compact Spaces
The purpose of this paper is to develop some properties of uniformly locally compact spaces. The terminology and symbology used are the same as those used in General Topology, by J. L. Kelley.
Date:
December 1971
Creator:
Page, Perman Hutson
System:
The UNT Digital Library
On Sets and Functions in a Metric Space
The purpose of this thesis is to study some of the properties of metric spaces. An effort is made to show that many of the properties of a metric space are generalized properties of R, the set of real numbers, or Euclidean n--space, and are specific cases of the properties of a general topological space.
Date:
December 1971
Creator:
Beeman, Anne L.
System:
The UNT Digital Library