We construct a compact subset K of the four dimensional Euclidean space with the following property: For all values of the parameter in an interval, the Vietoris-Rips complex of K has uncountably generated first homology. This answers a question that arose in work on persistent homology.
Neck-Pinching of $CP^1$-structures in the PSL(2,C)-character variety
A statistical approach to knot confinement via persistent homology
On imbedding of closed 2-dimensional disks into $R^2$
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