Semistratification of a topological space

Definition

A stratification of a topological space $X$ is defined as a rule that associates, to each open subset $U$ of $X$, a sequence $\{U_{n}\}_{n=1}^{\infty }$ of closed subsets of $X$, such that:

• $U_{n}\subseteq U$
• $U=\bigcup _{n=1}^{\infty }U_{n}$
• $U_{n}\subseteq V_{n}$ whenever $U\subseteq V$

A topological space which possesses a stratification is termed a stratifiable space.