Carmack On Future Graphics Engines

In a pure topological space, the limit is defined via the natural concepts of open sets and neighborhoods.

Textbooks often will define things in different manners, depending on their purposes.

Since we are dealing with objects that map to a subset of the reals, it seems obvious that computer set theory models would use manifolds, or even less general constructs (eg spaces with an associated distance function).

In R^k for instance, a less general notion of Cauchy sequences can also be utilitized to extract limit points.

 

Scott Topology has been used to do analysis of computable algorithms. It models the non-continuuous nature of computer logic in the reals.