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

Yoshimura, M.; Miwa, T.; Noiri, T.

Stud. Cercet. Mat. 47, No. 3-4, 353-358 (1995).

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.)

Keywords:

regular closed functions; \(g\)-closed functions; \(gr\)-closed functions; countably paracompact weakly normal spaces

Citations:

Zbl 0416.54005; Zbl 0578.54008