We prove an extrapolation theorem for the nonlinear m-term approximation with respect to a system of functions satisfying very mild conditions. This theorem allows us to prove end...
IsaPlanner is a generic framework for proof planning in the interactive theorem prover Isabelle. It facilitates the encoding of reasoning techniques, which can be used to conjectur...
In [1] it was developed o-minimal homotopy for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we also extend these res...
We prove a vector space analog of a version of the Kruskal-Katona theorem due to Lov´asz. We apply this result to extend Frankl’s theorem on r-wise intersecting families to vec...
We prove Helly-type theorems for line transversals to disjoint unit balls in Rd . In particular, we show that a family of n 2d disjoint unit balls in Rd has a line transversal if,...
Otfried Cheong, Xavier Goaoc, Andreas Holmsen, Syl...