Finely open morphisms of H-cones (Q790996)

The main result of this note establishes the equivalence, under certain assumptions, of the following properties of a H-map: finely open, finely or naturally non-constant, preserving the (semi-) polar sets under inverse image. One gets thus an effective generalisation of some previous results (on harmonic morphisms between harmonic spaces), obtained by: C. Constantinescu and A. Cornea, B. Fuglede, K. Oja. Specifically, the following hypotheses are abandoned: the base space is locally compact, the natural sheaf property and the natural continuity of the considered morphism.