## A generalization of regular closed and $$g$$-closed functions.(English)Zbl 0854.54020

Summary: A new class of functions called $$gr$$-closed functions is introduced as a generalization of both regular closedness [P. E. Long and L. L. Herrington, Rend. Circ. Mat. Palermo, II. Ser. 27, 20-28 (1978; Zbl 0416.54005)] and $$g$$-closedness [S. R. Malghan, J. Karnatak Univ., Sci. 27, 82-88 (1982; Zbl 0578.54008)]. The main result of this paper is that normality, weak normality, and countably paracompact weakly normal spaces are preserved under $$gr$$-closed continuous surjections.

### MSC:

 54C10 Special maps on topological spaces (open, closed, perfect, etc.) 54D10 Lower separation axioms ($$T_0$$–$$T_3$$, etc.)

### Citations:

Zbl 0416.54005; Zbl 0578.54008