Nowhere dense of linear subspace of at most n-1

Real Analysis
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Ram_1729
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Joined: Mon Dec 03, 2018 4:59 pm

Nowhere dense of linear subspace of at most n-1

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Post by Ram_1729 »

Let $W\subset \mathbb{R}^n$ be a linear subspace of dimension at most $n-1$. Which of the following statements are true ??
a)$W$ is nowhere dense
b)$W$ is closed
c)$\mathbb{R}^n-W$ is connected
d)$\mathbb{R}^n-W$ is not connected
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