Our interest in this paper is
in the mapping properties of minimal Hausdorff spaces; some of the results will
provide new characterizations of the classes of functionally compact and
C-compact spaces. Of more than secondary interest, it may be the primary
message of the paper, is the point of view adopted (and outlined in §2) in
studying the “divisibility” of the highly nondivisible class of minimal Hausdorff
spaces.