@misc{10481/98336, year = {2019}, url = {https://hdl.handle.net/10481/98336}, abstract = {We characterise the class of those Banach spaces in which every convex combination of slices of the unit ball intersects the unit sphere as the class of those spaces in which every convex combination of slices of the unit ball contains two points at distance exactly two. Also, we study when the convex combinations of slices of the unit ball are relatively open or have non-empty relative interior for different topologies, studying the relationship between them and studying these properties for L∞-spaces and preduals of L1-spaces}, organization = {Spanish MINECO/FEDER MTM2015-65020-P}, organization = {Junta de Andalucía/FEDER FQM-185}, publisher = {Springer Nature}, title = {Strong Diameter Two Property and Convex Combinations of Slices Reaching the Unit Sphere}, doi = {10.1007/s00009-019-1403-1}, author = {López Pérez, Ginés and Martín Suárez, Miguel and Rueda Zoca, Abraham}, }