A negative answer to the problem: are stratifiable spaces $M_1$?

TL;DR

This paper constructs a stratifiable space that is not an $M_1$-space, providing a counterexample to the assumption that all stratifiable spaces are $M_1$-spaces.

Contribution

It presents the first explicit example of a stratifiable space lacking the $M_1$ property, challenging previous conjectures.

Findings

Constructed a stratifiable space that is not $M_1$

Demonstrated the independence of stratifiability and $M_1$ property

Provided insights into the structure of stratifiable spaces

Abstract

In accordance with $M_3$-structures in paper [4], we construct a stratifiable space which is not $M_1$-spaces.