Another Note on M1-spaces

Abstract:

      In this note, we prove that, let f be a quasi-open, closed mapping from an M₁-space x onto a q-space (or a space of pointwise countable type) Y, then y is an M₁-space; which partially answers a classic problem. "Is the irreducible closed image of an M₁-space M₁?" (irreducible closed mapping→quasi-open mapping).