Welcome to mathimatikoi.org;a forum of university mathematics. Enjoy your stay here.

Nowhere dense of linear subspace of at most n-1

Real Analysis
Post Reply
Ram_1729
Articles: 0
Posts: 4
Joined: Mon Dec 03, 2018 4:59 pm

Nowhere dense of linear subspace of at most n-1

#1

Post by Ram_1729 » Sun Mar 31, 2019 7:43 pm

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
Post Reply