 Stratified pseudomanifold

An $N$-dimensional conically stratified space has a closed filtration $\varnothing =X_{-1}\subseteq X_0\subseteq \cdots \subseteq X_N=X$, with each nonempty $X_j\setminus X_{j-1}$ a $j$-manifold, $X_{N-1}=X_{N-2}$, and dense top stratum. At an $s$-stratum the conical link is a compact $(N-s-1)$-dimensional stratified pseudomanifold. In dimension zero a compact link is a finite set. Connected links are an additional normality condition, not part of this definition.