PFA and complemented subspaces of ℓ∞/c0

Alan Dow
2016 Journal of Logic and Analysis  
The Banach space ∞ /c 0 is isomorphic to the linear space of continuous functions on N * with the supremum norm, C(N * ). Similarly, the canonical representation of the ∞ sum of ∞ /c 0 is the Banach space of continuous functions on the closure of any non-compact cozero subset of N * . It is important to determine if there is a continuous linear lifting of this Banach space to a complemented subset of C(N * ). We show that PFA implies there is no such lifting. 2010 Mathematics Subject
more » ... Subject Classification 54A25 (primary); 03E35 (secondary)
doi:10.4115/jla.2016.8.2 fatcat:4wowmko6cbfatfavt7kmcd4bfu