In homotopy theory, phantom maps are continuous maps of CW-complexes for which the restriction of to any finite subcomplex is inessential. J. Frank Adams and Grant Walker produced the first known nontrivial example of such a map with finite-dimensional. Shortly thereafter, the terminology of "phantom map" was coined by Brayton Gray, who constructed a stably essential phantom map from infinite-dimensional complex projective space to . The subject was analysed in the thesis of Gray, much of which was elaborated and later published in. Similar constructions are defined for maps of spectra.