Index Analysis

Abstract

Rather than being restricted to asserting that a space, or a subset of a space, or a function, or any other item defined in terms of the structures at hand, does or does not have a certain property approach theory provides us with a canonical machinery by means of which we can define numerical indices of properties. The smaller an index is the better the property is approximated. In this chapter it becomes abundantly clear that the systematic use of indices lies at the heart of approach theory as they are built into the basics of the theory.

When you can measure what you are talking about and express it in numbers, you know something about it.

(Lord William Thomson Kelvin)

Finally - and frankly it’s a relief to see it - Karl Weierstrass sorted out the muddle in 1850 or thereabouts by taking the phrase “as near as we please” seriously. How near do we please?

(Ian Stewart)