Question

Vector space

Answer 1

the anticipation is killing me!!

Answer 2

Let \[V=\{f:(0,2) \rightarrow R| f\ is\ continuous\ and\ \lim_{x \rightarrow o^+}f(x)=\lim_{x \rightarrow 2^-}f(x)=0 \}\]Show that \[(V,+, \cdot, R)\]is vector space.

I know I have to show thatfor all x,y in V, x+y is in V and that for all x in V and all α in R, αx is in V.

Answer 3

hmm, so something of a visual like this maybe?