On M-structures and strongly regularly stratifiable spaces
This paper contributes to Ceder's problem: Is every \(M_ 3\)-space an \(M_ 1\)-space [\textit{J. G. Ceder}, Pac. J. Math. 11, 105-125 (1961; Zbl 0103.391); \textit{G. Gruenhage}, Topology Proc. 5, 77-104 (1980; Zbl 0463.54023); \textit{M. Itō}, Topology Appl. 19, 65-69 (1985)]? In a recent paper, the author introduced the concept of M-structures, and proved that every stratifiable space with an M-structure (called a space of class \({\mathcal M})\) is an \(M_ 1\)-space [ibid. 17, 63-89 (1984; Zbl 0536.54017)]. The main result of the present paper states that every strongly regularly stratifiable space [\textit{K. Tamano}, ibid. 16, 287-301 (1983; Zbl 0525.54020); Def. 4.2] is in the class \({\mathcal M}\). Further, a characterization of the class \({\mathcal M}\) in the class of all stratifiable space is given.
scientific article; zbMATH DE number 3895900