A smooth map $\lambda:V\to\bar{\Pi}$ is called a stratified $F$-fibration if

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  The restriction of $\lambda$ to any open $n$-cell $e\subset\bar{\Pi}$ is a trivial fibration with the fiber $F$;

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  for each integer pair $(l,k)$, $0\leq k\leq l\leq n$ there exists a smooth “model” map $\lambda_{l,k}:V_{l,k}\to\Pi_{l,k}$, where $\Pi_{l,k}\approx\mathbb{R}^{k}\times\Sigma^{l-k}_{0}\times[0,+\infty)^{n-l}$, such that any $(l,k)$-point of $\bar{\Pi}$ has a neighborhood $U\supset x$ such that

  $$\lambda|_{U}:\lambda^{-1}(U)\to U$$

  is diffeomorphic to the model map. The model map depends only on $l$ and $k$.

The map $\lambda_{l,k}$ is called the $(l,k)$-fiber degeneration; the fiber $F_{l,k}=\lambda^{-1}_{l,k}(x)$ is called the $(l,k)$-fiber of $\lambda$.