I received my PhD in mathematics at the University of Missouri at Columbia on August 5, 1955. My dissertation was entitled Metric Foundations of Elliptic 2-space.
I recall that I was very delighted on my first encounter with topology. I had just completed my first semester of the usual graduate course in Real Analysis. My study in Real Analysis had led me to an independent journey into General Topology (or Point-Set Topology). I was in awe as this topology simplified and clarified many of the tedious basic concepts in Analysis. I took several courses in topology under Profs Utz and Blumenthal – including a course in Topological Dynamics, which was the specialty of Prof Utz. I also took an Individual Work course with Prof Utz in which I studied the book Topological Groups by L S Pontryagin, a blind mathematician.
When arriving at the University of Florida in September of 1955, I found (at that time) there was no one in the mathematics department who was particularly interested in teaching Topology. So I was delighted to be able to teach the graduate level course in Topology in the fall and spring semesters. I continued to teach this graduate course in Topology for several years, and quickly added an undergraduate course in Topology. I particularly enjoyed teaching this undergraduate course. I was so happy to notice many of the outstanding mathematics majors fully appreciated the beauty of this abstract mathematics even though they had not studied Advanced Calculus yet. Many of these students fell in love with this branch of pure mathematics; and I was happy for them, knowing how it would simplify their journey through Advanced Calculus and graduate level Real Analysis (and in Complex Analysis) if they continued in graduate work.
This is a picture of me taken at the University of Missouri in 1955. I had just received the PhD degree under Dr. Leonard Blumenthal who was born in Athens, Georgia in 1902. Blumenthal received the BS from Georgia Tech in 1923, a MA from Chicago in 1924 and a PhD from John Hopkins in 1927, with a dissertation entitled Lagrange Resolvents in Euclidean Geometry. After stints at the Rice Institute, as National Research Fellow at the Institute for Advanced Study, and in Vienna during 1934 – 1935, Blumenthal joined the University of Missouri as an Assistant Professor in 1936. He was promoted to Associate in 1939 and to Professor in 1944. [Notes on Dr. Blumenthal were taken from a paper that Prof Paul Ehrlich who had earlier been a Professor at the University of Missouri, wrote on the occasion of my retirement in December 2007.]
My six masters candidates wrote their theses on topics in topology. They are enumerated as follows:
|William Brown Stelwagon, Jr.,||Convergence and Denseness in Lattices, June, 1961|
|Arnold Joseph Insel,||Compactness and Convergence in Complete Lattices, June, 1962|
|Charles Harwick Bertness,||Local Properties of Topological Spaces, August, 1964|
|Dennis Mario Parra,||Ecart Spaces, April, 1965|
|Bruce Peter Walek,||Nets, Filters and Syntaxes in Topological Spaces, August, 1965|
|Joan Marie Golliday,||Extended Topologies, August, 1966|
Arnold Joseph Insel had the results of his master’s research published in the Proceedings of the American Mathematical Society in 1963 under the title A Compact Topology for a Lattice which he footnoted as research that he had done under the direction of Professor T. O. Moore.
My book Elementary General Topology published by Prentice Hall came out in 1964.