Professor John Horvath's commitment towards a universal use of distribution theory proceeded concurrently in two directions. The first one investigated the nature of distributions and the spaces to which they belong, and, more generally, the theory of locally convex topological vector spaces. Around 1954 Laurent Schwartz encouraged him to write an "introductory textbook," which appeared in 1966 as "Topological Vector Spaces and Distributions, vol. I." The first 3 chapters treat Banach spaces and—in the spirit of Nicolas Bourbaki—general topology, locally convex topological vector spaces and duality. Chapter 4 dealt with distributions, which content he later modified and delivered in lecture series, making his contribution to that field widely known.
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