  In this note, we attack a question posed ten years ago by Tsukiyama about the
injectivity of the so- called Forgetable map. We show that we can insert the
Forgetable map in an exact sequence and that the problem can be reduced to the
computation of the sequence which turns out unexpectedly to be related to the
phantom map problem and the famous Halperin conjecture in rational homotopy
theory.
