Resumen de ℵ-injective Banach spaces and ℵ-projective compacta
Antonio Avilés, Félix Cabello Sánchez 
, Jesús María Fernández Castillo , Manuel González Ortiz , Yolanda Moreno Salguero
A Banach space E is said to be injective if for every Banach space X and every subspace Y of X every operator t:Y→E has an extension T:X→E. We say that E is ℵ-injective (respectively, universally ℵ-injective) if the preceding condition holds for Banach spaces X (respectively Y) with density less than a given uncountable cardinal ℵ. We perform a study of ℵ-injective and universally ℵ-injective Banach spaces which extends the basic case where ℵ=ℵ1 is the first uncountable cardinal. When dealing with the corresponding "isometric" properties we arrive to our main examples: ultraproducts and spaces of type C(K). We prove that ultraproducts built on countably incomplete ℵ-good ultrafilters are (1,ℵ)-injective as long as they are Lindenstrauss spaces. We characterize (1,ℵ)-injective C(K) spaces as those in which the compact K is an Fℵ-space (disjoint open subsets which are the union of less than ℵ many closed sets have disjoint closures) and we uncover some projectiveness properties of Fℵ-spaces.
