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 $\{U_n{\}}_{n=1}^{\mathrm{\infty }}$ of subsets, such that:

• $\overline{U_n}\subset U$
• $U=\bigcup _{n=1}^{\mathrm{\infty }}{U}_n$
• $U_n\subset V_n$ whenever $U\subset V$

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