Topology Proceedings Document # baak-28
 Electronic Version 24 Summer (1999)

## Towards computing homology from finite approximations

### V. Robins

We consider the problem of extrapolating the homology of a compact metric space from a finite point-set approximation. Our approach is based on inverse systems of \epsilon-neighborhoods and inclusion maps. We show that the inclusion maps are necessary to identify topological features in an \epsilon-neighborhood that persist in the limit as \epsilon --> 0. We outline a possible algorithm for computer implementation. As test examples, we present data for some iterated function system relatives of the Sierpinski triangle.