Phantom map

In homotopy theory, phantom maps are continuous maps defined on a direct limit of spaces in which each restriction is inessential. The first known example involved the filtration of a finite dimensional CW complex by finite sub-complexes ([AW]). The first example in which the filtration was by the skeleta led to the name [G]. In this case, a stably essential map was constructed from infinite dimensional complex projective space to S^3. The subject was analysed in the thesis of Gray, much of which was further developed and later published in [GM]. Similar constructions are defined for maps of spectra [L]