Document # baak-28
Electronic Version 24 Summer (1999)
Towards computing homology from finite approximations
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.
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Topology Proceedings Electronic Version
Copyright © 2001
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Date published electronically: March 5, 2001.