A lemma on extending functions into F -spaces and homomorphisms between Stone–Čech remainders

I. Protasov, J. Pym, D. Strauss
2000 Topology and its Applications  
This papers contains two main results. The first is a theorem about continuous functions from a countably compact Hausdorff space into a compact F -space, which has applications to the algebraic properties of the Stone-Čech compactification βS of a discrete semigroup S. The second main result shows that many continuous homomorphisms from S * to G * have to arise from homomorphisms mapping S to G, where S is a discrete semigroup and G is a discrete group and S * denotes βS \ S. The second result
more » ... is related to the first because it uses it at a crucial point.
doi:10.1016/s0166-8641(99)00061-9 fatcat:44wvr2qgabeybdprslzheq6e5q