(2) Let (X,r)be a topological space, If for every A open set, and x E A", 3 Ux and Vy open sets, such that x E Ux, AC Vy, and Un V, = 4. The space is called: (a) Hausdorff Space (b) Regular space (c) T1-space (d) Normal space

Let V be the set of all positive real numbers. Determine whether V is a vector space with the operations shown below. x+y=xyAddition cx=xcScalar multiplication If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.

Which vector spaces are isomorphic to R6? a M2,3 b P6 c C[0,6] d M6,1 e P5 f C[3,3] g {(x1,x2,x3,0,x5,x6,x7):xiisarealnumber}

Prove that in a given vector space V, the zero vector is unique.