Extending complex functions f:C-->C into f^:C^-->C^ Hi, All: I have a function f: ℂ-->ℂ' , i.e., a complex-valued function (use ℂ,ℂ' to make a distinction between the complexes as domain and codomain respectively), and i want to extend it into the Riemann Sphere ℂ^, i.e., I am looking for f^ such that f^|ℂ=f. If I remember correctly, a necessary and sufficient condition for extensibility is that f must be a proper function, i.e., that for every K compact in ℂ' is sent to a compact set in ℂ, i.e., f-1(K) is compact in ℂ? I think this somehow had to see with ℂ^ being the 1-pt compactification of ℂ; is this correct? If so, anyone have a ref. for the proof, if not, could someone please let me know what the correct result is? Thanks.