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Let $V$ be a vector space over $F$ where $F$ is infinite. Are there proper subspaces $\{W_i\}_{i \in I}$ such that $V = \bigcup_{i \in I} W_i$ where $I$ is countable?

If $V$ is a vector space over a finite field with $\dim V > 1$, this is clearly true since $V$ has finitely many elements, we have $V = \bigcup \operatorname{span}(v)$ where $v \ne 0$.

Cameron Buie
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anon
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    http://math.stackexchange.com/questions/145869/a-finite-dimensional-vector-space-cannot-be-covered-by-finitely-many-proper-subs?rq=1 http://math.stackexchange.com/questions/10760/a-vector-space-over-r-is-not-a-countable-union-of-proper-subspaces?lq=1 – tessellation Jun 24 '13 at 04:11
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    Please check the suggestions of previous questions before posting. – tessellation Jun 24 '13 at 04:12
  • @tessellation What suggestions? – anon Jun 24 '13 at 04:17
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    Whenever you are asking any question just above the space of writing stackExchange will automatically show you some suggestions, These are the questions asked previously about the topic you are posting. Just go through them to see if the question is already asked or not. In your case (in the two links above ) this question has already been asked twice. Its just to avoid repeattation of any question. – tessellation Jun 24 '13 at 04:25

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