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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 Subjectdoi:10.4115/jla.2016.8.2 fatcat:4wowmko6cbfatfavt7kmcd4bfu