Poincare Project: Metric Spaces

A surface is more than just a set of points. Points on a surface have a notion of closeness that doesn't exist with a set unless we add some structure.

One way we can introduce the idea of closeness is to introduce the idea of the distance between points. That is, a function d that gives us a number for any pair of points.

To be a distance function, our function must meet some additional requirements:

A distance function is often called a metric. A set of points with a distance function is called a metric space.

A metric space clearly has a notion of closeness. A point y is closer to x than z is if d(y,x)<d(z,x).

UPDATE: next post

The original post was in the category: poincare_project but I'm still in the process of migrating categories over.