It is known that a Banach space contains an isomorphic copy of $ c_0 $ if, and only if, it can
be equivalently renormed to be almost square. We introduce and study transfinite versions …

We introduce slicely countably determined points (SCD points) of a bounded and convex
subset of a Banach space which extends the notions of denting points, strongly regular …

We study versions of the diameter two properties where the diameter of slices, weakly
relatively open subsets, or convex combinations of slices of the unit ball is attained. We also …

We study transfinite analogues of the symmetric strong diameter two property. We
investigate the stability of these properties under c 0, ℓ∞ sums and under projective tensor …