On Continuity (1960-1969)

"If each segment of a broken line in space be given the direction determined in passing continuously from one terminal to the other, then the algebraic sum of the projections of the segments upon any directed line equals the projection of the closing line. If the broken line in question should be a closed polygon, the sum of the projections of the sides upon any directed line is zero." (William L Schaaf, "Analytic Geometry; a college course guide", 1962) 

"Analysis is primarily concerned with limit processes and continuity, so it is not surprising that mathematicians thinking along these lines soon found themselves studying (and generalizing) two elementary concepts: that of a convergent sequence of real or complex numbers, and that of a continuous function of a real or complex variable." (George F Simmons, "Introduction to Topology and Modern Analysis", 1963)

"When a curve approaches an axis or any other straight line in this fashion, the line is said to be an asymptote of the curve. As a working definition, we may say: An asymptote of a curve is any straight line which a curve approaches continuously as the curve moves on to infinity." (William L Schaaf, "The Calculus, a college course guide", 1963)

"A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint." (Lotfi A Zadeh, "Fuzzy Sets", 1965)

"General or point set topology can be thought of as the abstract study of the ideas of nearness and continuity. This is done in the first place by picking out in elementary geometry those properties of nearness that seem to be fundamental and taking them as axioms." (Andrew H Wallace, "Differential Topology: First Steps", 1968)