determine whether w={f:f(x)greater than or equal to 0} is a subspace of C, the set is continuous functions on the real numbers

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- Feb 21st 2011, 04:41 PMrabih2011subspaces
determine whether w={f:f(x)greater than or equal to 0} is a subspace of C, the set is continuous functions on the real numbers

- Feb 21st 2011, 04:58 PMDrSteve
If f is in w, think about the function -f.

- Feb 21st 2011, 07:57 PMRaoh
In other words,is $\displaystyle w$ closed under scalar multiplication ?

- Feb 21st 2011, 10:05 PMFernandoRevilla

No, it isn't. Look at**DrSteve**'s post. For example choose $\displaystyle f(x)=1$ for all $\displaystyle x\in \mathbb{R}$ then, $\displaystyle f\in W$ however $\displaystyle [(-1)f](x)=(-1)f(x)=(-1)\cdot 1=-1$ . That is, $\displaystyle (-1)f\not\in W$ .

Fernando Revilla - Feb 22nd 2011, 02:35 AMAckbeet
- Feb 22nd 2011, 10:43 AMRaoh
My question was meant to help the OP'er.

- Feb 22nd 2011, 11:30 AMFernandoRevilla

Sorry, by error I thought your post was from the original poster. :)

Fernando Revilla - Feb 22nd 2011, 01:38 PMDrSteve
Wow - it's not too hard to get thanked around here - very polite group!