The purpose of this paper is to develop a geometry based on fourteen axioms and four undefined terms.

Thesis (Ph. D.)--Oregon State University, 1970. / Typescript (photocopy). Includes bibliographical references (leaf 146). Also available on the World Wide Web.

Thesis--Helsinki.

This thesis explores some results of two topological spaces.

This paper is an algebraic study of selected properties of semigroups. Since a semigroup is a result of weakening the group axioms, all groups are semigroups. One facet of the paper is to demonstrate various semigroup properties that induce the group axioms.

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.

The problem with which this study is concerned is the development of a mathematical model and theory of teaching. The mathematical model consists of a set of abstract axioms. The fundamental elements or terms of the axioms are undefined. These primitive or undefined terms obtain their definitions only implicitly through the axioms.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

A turtle geometric construction on the plane, called a polynomial generated polygon (PGP) and represented by Pf,pm, is generated from the sequence obtained from evaluating f(x) ∈ Z[x] over Z modulo pm where p is a prime and m ∈ N. Computational methods are developed to pre-calculate the symmetries exhibited by Pf,pm for a given f and pm. These include procedures to find whether Pf,pm is bounded or unbounded, the degree of rotational symmetry present, whether lines of reflectional symmetry can be observed, and in the case of Pf,pm unbounded, whether the PGP has a glide reflection. Methods are also sought to find a suitable f and pm to produce a desired 'feasible' shape in a PGP construction, and how the same shape might be generated modulo pm+k if it cannot be produced modulo pm.

Axioms for a topological space are generally based on neighborhoods where "neighborhood" is an undefined term. Then, limit points are defined in terms of neighborhoods. However, limit points seem to be the basic concept of a topological space, rather than neighborhoods. For this reason, it will be attempted to state a set of axioms for a topological space, using limit point as the undefined concept, and to delete the idea of neighborhoods from the theory.