Donald Hartig

My Ph. D. Thesis, written under the direction of Ky Fan at the University of California at Santa Barbara, examined certain properties characterizing the map that associates with a compact space X, the space C(X) of continuous scalar-valued functions on X. At the same time, a continuous function f from X to Y is mapped to the operator T from C(Y) to C(X) defined by T(g) = g composed with f. My thesis was published in Studia Mathematica a lifetime ago. An elementary exposition of the properties of the functor described above can be found in An Important Functor in Analysis and Topology, American Math Monthly, 85(1978). Subsequent research was devoted to relationships between X and C(X), an area that was extremely popular in the 1960s. In particular, connectedness properties of X can be characterized in various ways. See Local connectedness and pseudocompactness in completely regular spaces, Proc Amer Math Soc, 68(1978) and A Banach space property of C(X) characterizing local compactness in X, Pure and Applied Math Sci, 12(1980). I also published an interesting article entitled Cones in L-Spaces in the Bulletin of the Instutute of Mathematics of the Academia Sinica (Vol 2 No 2, 1974). This was dedicated to my advisor in the occasion of his 65th birthday.

For work more closely related to my teaching see The Riesz Representation Theorem Revisited, American Math Monthly, 90(1983), On the Differentiation Formula for Sine, American Math Monthly, 96(1989), and L’Hopital’s Rule via Integration, American Math Monthly, 98(1991).

In the late 1980s and early 1990s I became intensly interested in measure theory, presenting an occasional paper and working on questions associated with the validity of the Lebesgue Convergence Theorem in a general topological measure space. At about the same time I became an active participant in the Calculus reform movement investigating the possibilities associated with advances in computer software and hand calculators. See PROFESSIONAL ACTIVITIES.