Union of uncountably many subspaces Supposing, $\{V_t\}, t > 0$ are an uncountable number of linear subspaces of $\mathbb{R}^n$. If $\bigcup_{t>0} V_t = \mathbb{R}^n$ is it true that $V_T = \mathbb{R}^n$ for some $T>0$? 
Any help is appreciated. Thanks.
EDIT: I have forgot to add the condition that $V_t$ are increasing.  

In general the answer is no. Consider family of subspaces of the form
$$
V_t=\{x\in\mathbb{R}^n:x_1\cos\frac{2\pi}{t+1}+x_2\sin\frac{2\pi}{t+1}=0\}
$$
