# Robert Raphael: On the countable lifting property for C(X)

Place:  Fields Institute (Room 210)

Date: 17-April-2015 (13:30-15:00)

Speaker: Robert Raphael

Title: On the countable lifting property for C(X)
Abstract: Suppose that Y is a subspace of a Tychonoff space X so that the induced ring homomorphism $C(X) \rightarrow C(Y)$ is onto. We show that a countable set of pairwise orthogonal functions in C(Y) can be lifted to a pairwise orthogonal preimage in C(X). The question originally arose in vector lattices. Topping published the result for vector lattices using an erroneous induction, but two years later Conrad gave a counterexample. This is joint work with A.W.Hager.