let (x,d) be a metric space. define a flow on (x,d)

Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1) is a vector space. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.

one example of a 4-dimensional vector space that is not R 4

28. Is C a real vector space? Explain.