Caratheodory-type Theorems a la Barany
We generalise the famous Helly-Lovasz theorem leading to a generalisation of the Barany-Carath,odory theorem for oriented matroids in dimension a parts per thousand currency sign3. We also provide a non-metric proof of the latter colourful theorem for arbitrary dimensions and explore some generalisations in dimension 2.
caratheodory-type theorems oriented matroids colourful theorems helly-type theorems abstract convexity separoids