Subject: Re: question and workshop Date: Sat, 12 May 2001 13:49:20 -0400 (EDT) From: Claude Schochet To: Don Davis From: Michael Cole Does anyone know if there is any terminology in the literature to describe a map of spaces f:X \to Y for which the image of f in Y has the quotient space topology of X (for example, if X is quasicompact and Y is Hausdorff)? Surely someone must have coined a term for such maps. I used "relatively open" for this in my paper "The Fine Structure of the Kasparov Groups I: continuity of the KK-pairing ", JFA, to appear. (It will be on xxx soon.) It is easy to show that any *-homomorphism f: A \to B of C*-algebras has this property. This yields easy consequences re maps induced on function spaces.