Re: R^4 subspace question

Quote:

Originally Posted by

**transgalactic** $\displaystyle dim(W\cap U\cap V)\geq17$ is it correct?

Impossible, $\displaystyle W\cap U\cap V\subset \mathbb{R}^4$ so, $\displaystyle \dim (W\cap U\cap V)\leq 4$ .

Re: R^4 subspace question

indeed, we have 4 = dim(R^4) ≥ dim(U+V) = dim(U) + dim(V) - dim(U∩V) = 6 - dim(U∩V).

this means that dim(U∩V) ≥ 6-4 = 2.

now we also have 4 ≥ dim((U∩V)+W) = dim(U∩V) + dim(W) - dim((U∩V)∩W) ≥ 5 - dim(U∩V∩W).

this means that dim(U∩V∩W) ≥ 5-4 = 1.

Re: R^4 subspace question

ok i understand now

thanks