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.