On M-structures (Q791917)

The author defines the concept of ''M-structure'' for topological spaces and proves several interesting results about the class \({\mathcal U}\) of stratifiable spaces with M-structures. In particular, each \(M\in {\mathcal U}\) is an \(M_ 1\)-space, stratifiable \(\mu\)-spaces (i.e. spaces embeddable in a countable product of paracompact spaces which are countable unions of closed metrizable subspaces) belong to \({\mathcal U}\), \({\mathcal U}\) is closed with respect to countable products and subspaces. (It is not known if \(M_ 1\)-spaces have M-structures nor if closed continuous maps preserve M-structures.)