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.