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Stefan Kohl
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closed Closed subsets of Whitney objects

Let $M$ be a smooth manifold and $X\subset M$ be a Whitney objectWhitney object, i.e. a subset with a Whitney stratification $\mathcal{S}$. If $W\subset X$ is a closed subset of $X$ such that for each stratum $S\in\mathcal{S}$ the intersection $W\cap S$ is a smooth submanifold of $M$, then is it true that $W$ is also a Whitney object with the decomposition $\mathcal{S}_{W}=\{S\cap W\mid \forall S\in\mathcal{S}\}$?

closed subsets of Whitney objects

Let $M$ be a smooth manifold and $X\subset M$ be a Whitney object, i.e. a subset with a Whitney stratification $\mathcal{S}$. If $W\subset X$ is a closed subset of $X$ such that for each stratum $S\in\mathcal{S}$ the intersection $W\cap S$ is a smooth submanifold of $M$, then is it true that $W$ is also a Whitney object with the decomposition $\mathcal{S}_{W}=\{S\cap W\mid \forall S\in\mathcal{S}\}$?

Closed subsets of Whitney objects

Let $M$ be a smooth manifold and $X\subset M$ be a Whitney object, i.e. a subset with a Whitney stratification $\mathcal{S}$. If $W\subset X$ is a closed subset of $X$ such that for each stratum $S\in\mathcal{S}$ the intersection $W\cap S$ is a smooth submanifold of $M$, then is it true that $W$ is also a Whitney object with the decomposition $\mathcal{S}_{W}=\{S\cap W\mid \forall S\in\mathcal{S}\}$?

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David C
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Let $M$ be a smooth manifold and $X\subset M$ isbe a Whitney object, i.e. a subset with a Whitney stratification $\mathcal{S}$. If $W\subset X$ is a closed subset of $X$ such that for each stratum $S\in\mathcal{S}$ the intersection $W\cap S$ is a smooth submanifold of $M$, then is it true that $W$ is also a WhinteyWhitney object with the decomposition $\mathcal{S}_{W}=\{S\cap W\mid \forall S\in\mathcal{S}\}$?

Let $M$ be a smooth manifold and $X\subset M$ is a Whitney object, i.e. a subset with a Whitney stratification $\mathcal{S}$. If $W\subset X$ is a closed subset of $X$ such that for each stratum $S\in\mathcal{S}$ the intersection $W\cap S$ is a smooth submanifold of $M$, then is it true that $W$ is also a Whintey object with the decomposition $\mathcal{S}_{W}=\{S\cap W\mid \forall S\in\mathcal{S}\}$?

Let $M$ be a smooth manifold and $X\subset M$ be a Whitney object, i.e. a subset with a Whitney stratification $\mathcal{S}$. If $W\subset X$ is a closed subset of $X$ such that for each stratum $S\in\mathcal{S}$ the intersection $W\cap S$ is a smooth submanifold of $M$, then is it true that $W$ is also a Whitney object with the decomposition $\mathcal{S}_{W}=\{S\cap W\mid \forall S\in\mathcal{S}\}$?

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yangyang
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closed subsets of Whitney objects

Let $M$ be a smooth manifold and $X\subset M$ is a Whitney object, i.e. a subset with a Whitney stratification $\mathcal{S}$. If $W\subset X$ is a closed subset of $X$ such that for each stratum $S\in\mathcal{S}$ the intersection $W\cap S$ is a smooth submanifold of $M$, then is it true that $W$ is also a Whintey object with the decomposition $\mathcal{S}_{W}=\{S\cap W\mid \forall S\in\mathcal{S}\}$?