3 problems
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The conjecture that the derived Mapper convergence rate is not optimal
Assume that and are known, and let be chosen of order … so that the first two terms in the risk bound are of order , w…
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Steinhaus–Čech equivalence conjecture in Euclidean space
Steinhaus–Čech equivalence conjecture. The Čech filtration constructed from is isomorphic to the cover filtration on constructed from .
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Steinhaus–Čech equivalence conjecture for finite point sets
Steinhaus–Čech equivalence conjecture. The Čech filtration and the Steinhaus Nerve constructed from its terminal cover are isomorphic.