Type: Article

Splitting chains, tunnels and twisted sums

Cabello-Sánchez, F., Avilés, A., Borodulin-Nadzieja, P., Chodounsky, D., Guzmán, O.;

Abstract:

We study splitting chains in P(omega), that is, families of subsets of omega which are linearly ordered by subset of* and which are splitting. We prove that their existence is independent of axioms of ZFC. We show that they can be used to construct certain peculiar Banach spaces: twisted sums of C(omega*) = l(infinity)/c(0) and c(0)(c). Also, we consider splitting chains in a topological setting, where they give rise to the so called tunnels.