Persistent Homology and the Upper Box Dimension
نویسنده
چکیده
We introduce a fractal dimension for a metric space based on the persistent homology of subsets of that space. We exhibit hypotheses under which this dimension is comparable to the upper box dimension; in particular, the dimensions coincide for subsets of R whose upper box dimension exceeds 1.5.
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عنوان ژورنال:
- CoRR
دوره abs/1802.00533 شماره
صفحات -
تاریخ انتشار 2018