Figure 1 Example of persistent homology for a point cloud. (a) A finite set of points in R 2 (for (cid:2) = 0) and a nested sequence of spaces obtained from it (from (cid:2) = 0 to (cid:2) = 2.1). (b) Barcode for the nested sequence of spaces illustrated in (a). Solid lines represent the lifetime of components, and dashed lines represent the lifetime of