Stratification 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 open subsets, such that:

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

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