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.  

Consider a bijection $\phi:(0,+\infty)\to\mathbb R^n$ and for each $t>0$ let $V_t$ be the subspace of $\mathbb R^n$ spanned by $\phi(t)$.
