Connected Sets and the AMS , 1901 – 1921

C hapter 1 of Kelley’s famous book General Topology introduces the most fundamental concepts of a topological space. One such notion is defined as follows [1]: A topological space (X, τ) is connected if and ony if X is not the union of two nonvoid separated subsets, where A and B are separated in X if and only if A∩ B = œ and A∩ B = œ. As usual, Y denotes the closure of a subset Y of X. Kelley’s book has been a staple for several generations of graduate students, many of whom must have wondered what this formal definition had to do with their intuitive notion of a connected set. Frequently, such queries can be answered by an historical investigation, and the aim here is to trace the development of the formal concept of a connected set from its origins in 1901 until its ultimate ascension into the ranks of mathematical concepts worthy of study for their own sake twenty years later. Much of this development took place at the University of Chicago under E. H. Moore, and the evolution of connected sets exemplifies one specific way in which ideas that germinated there would be promulgated by his descendants. Although Moore exerted little direct influence, his department’s core of outstanding graduate students, like the well-known Oswald Veblen, and its cadre of small-college instructors and high school teachers from across the country who pursued degrees during summer sessions,