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math.CO2025
Excursions in Sylvester-Gallai land
Imre Barany, Julia Q. Du, Dan Schwarz +2
The Sylvester-Gallai theorem states that for a finite set of points in the plane, if every line determined by any two of these points also contains a third, then the set is necessa…
math.FA2025
On Klee's problem of convex bodies in Banach spaces
Lixin Cheng, Chunlan Jiang, Liping Yuan
It is well known that every convex body in a finite dimensional normed space can be uniformly approximated by strictly convex and smooth convex bodies. However, in the case of infi…
math.CO2025
Orthogonally connected sets
Xuemei He, Xiaotian Song, Liping Yuan +1
In this paper, we further investigate the orthogonally connected sets and establish necessary and sufficient conditions for a set to be staircase connected.