The inverse image
preservation problem of R-compact (realcompact) spaces has been studied by R.
Blair, N. Dykes, and T. Isiwata. In this paper their results are drawn together, and
the inverse images of E-compact spaces under certain kinds of mappings
are studied. Actually, a more general question, concerning the notion of
E-perfect mappings, is considered. (The inverse image of an E-compact
space under an E-perfect mapping is E-compact.) Classes of hereditarily
E-compact spaces and their inverse images under certain mappings are also
studied.
