The Seven C’s of Analysis

Abstract

The current chapter explains key concepts of mathematical analysis summarized by the six adjectives convergent, complete, closed, compact, continuous, and connected. A later chapter will add to these six c’s the seventh c, convex. At first blush these concepts seem remote from practical problems of optimization. However, painful experience and exotic counterexamples have taught mathematicians to pay attention to details. Fortunately, we can benefit from the struggles of earlier generations and bypass many of the intellectual traps.