Subject: RE: two questions From: "Neil Strickland" Date: Tue, 5 Oct 2004 21:44:46 +0100 To: "Don Davis" >> Let Y_0 --> Y_1 --> Y_2 --> ... >> be a sequence of spectra and maps. >> If X is a spectrum, what is the relation between >> lim_{->} [X,Y_i] and [X, lim_{->} Y_i] ? I don't know a systematic answer, but here is an important example. Let H be the mod p Eilenberg-MacLane spectrum. It is known that [H,X]=0 for any finite X. (I think this is in Doug Ravenel's "Localization with respect to certain periodic homology theories"). We can write H = colim_n X_n with X_n finite, and then [H,colim X_n] = [H,H] = Z/p, but colim [H,X_n] = 0. Neil Strickland